In late 2005, playwright Yasmina Reza was approached by a German theatre director who wanted to commission a new work from her. "I said, 'No, I'm tired, I've got too much on; I don't want to do it,'" Reza says, sitting in the corner of a darkened hotel bar in her native Paris. She gives a dismissive flap of her hand, as if reliving the refusal. But then, something happened to change her mind.

"There was a little incident in the life of my son," she says, refilling her cup of herbal tea from an Oriental-style teapot as she talks. "He was then about 13 or 14 and his friend was in a fight with another friend; they exchanged blows and my son's friend had his tooth broken. A few days later, I met with the mother of this boy in the street. I asked her how her son was, if he was better, because I knew they'd had to do something to the tooth – they'd had to operate or something. And she said, 'Can you imagine? The parents [of the other boy in the fight] didn't even call me.'"

Reza looks at me steadily, brown eyes unblinking, as if to underline the gravity of the situation. But then her mouth twitches at the corner and she breaks out into a wide grin.

"It was suddenly, click! I thought, 'This is an incredible theme.'" She almost bounces on her chair at the memory, her hair swishing as though mirroring her enthusiasm. "So I asked the Germans if it was still possible to do a play and they said, 'It's possible, but you have to do it by April.'"

Reza then wrote the entire thing in three months. "No method," she says blithely. "I just wrote it."

The resulting work was Le Dieu du carnage (God of Carnage), one of the most popular and acclaimed plays of the last 10 years, which has seen several theatrical productions and has now been made into a film directed by Roman Polanski, starring Kate Winslet, Christoph Waltz, John C Reilly and Jodie Foster as warring, middle-class couples who meet to discuss their children's playground fight.

Reza's play charts the course of this superficially civilised get-together, which soon degenerates into an evening of mutual dislike and name-calling. By the end of the encounter, their acid dialogue has burned through the veneer of smug, bourgeois respectability, with alternately comic and uncomfortable consequences.

In London, where the play had its premiere in 2008 (following a translation by Reza's long-time collaborator, Christopher Hampton), it was a critical and commercial success. In the Guardian, Michael Billington hailed Reza as "a born satirist"; others proclaimed themselves "delighted by her incisive observation" and "shrewd humour". It scooped an Olivier for best new play and when God of Carnage transferred to Broadway in 2009, it won a Tony and became the third-longest-running production of the decade.

The Polanski film, called simply Carnage, is remarkably faithful to the original. Despite the setting having been transferred from Paris to Brooklyn, much of the dialogue remains and the bulk of the action takes place within four, claustrophobic apartment walls.

"I realised everything transposed immediately from Paris to Brooklyn," says Reza, who adapted the screenplay with Polanski. "We wrote it in French first but he wanted to do it with English actors because he was more at ease with that. So he translated it."

It is the first time 52-year-old Reza has given permission for one of her plays to be adapted for the big screen. Art, the play she wrote in 1994 and for which she is best known, has been translated into more than 30 languages, grossed almost £200m worldwide and won the theatre world's triple crown: the French Molière award, the British Olivier award and, in a first for a non-English-language piece, the American Tony award.

Four more sell-out plays have followed, including Life x 3. Audiences flocked to theatres on both sides of the Channel. In France, a country in which commercial success in the arts is frequently equated with creative failure, Reza none the less became a star. The daily newspaper Libération once compared the media circus surrounding the production of one of her plays to the release of the latest Harry Potter.

She says she has been "inundated" by requests from film-makers who want to adapt her work, all of which she had refused until now. So why say yes this time?

"Polanski," she replies without hesitation. "I adore him." It is not the first time the two of them have joined forces – Reza translated Polanski's stage version of Kafka's Metamorphosis in the late 1980s at his request – but I wonder if she had any scruples about working with him either time. "Scruples?" she asks, apparently mystified. Yes, did she feel uncomfortable about the fact that Polanski is wanted in the States on six criminal counts, including the rape of a 13-year-old girl (as a result of which, Carnage had to be filmed in Paris)? "No, I had no scruples," Reza replies. "It went very well writing with him… we are identical. We don't discuss 'the meaning'; we discuss the instinct."

It is a strangely amoral response from the woman who once reportedly said: "Theatre is a mirror, a sharp reflection of society. The greatest playwrights are moralists." And it is true that in her plays, pretension, hypocrisy and emotional carelessness are skewered with devastating accuracy. In God of Carnage, the character who provides much of the comic fodder is Alain, the cynical lawyer who spends much of his time on the phone defending the disastrous side-effects of a drug marketed by a dodgy pharmaceutical company.

In Life x 3 (written in 2000), Reza presented three versions of the same point-scoring dinner party, again laying bare the falseness of social nicety and the savagery that lies beneath its surface. It is possible that her background – Reza was raised in France by her Russian-Iranian engineer father, who died several years ago, and Hungarian violinist mother – gives her a unique perspective. Although Reza says she "feels French" and is fluent in her country's socio-cultural subtleties, her perspective remains that of an acute and wryly interested observer.

Does she still consider herself a moralist? She smiles. "There are all these university theses that say I'm a moralist. I don't know if I am or not. Perhaps…" She lets the thought hang, taking another sip of her tea.

In fact, she positively eschews the notion that she sets out to write plays with "big ideas". "You know, critics in general always have a tendency to give a sociological dimension to my work. For me, I'm thrilled they say that, but it's not that that animates me. What motivates me most is writing about people who are well brought up and yet, underneath that veneer, they break down. Their nerves break down. It's when you hold yourself well until you just can't any more, until your instinct takes over. It's physiological."

It is for this reason, she says, that she never seeks to explain or deconstruct her characters' backgrounds for the audience. "I'm not interested in what they were like as children, in psychoanalysis, because writing is totally instinctive. I work like a painter. If a painter is doing a portrait of someone, he's not interested in their childhood; he paints what he sees. There's no explanation because it doesn't mean anything."

The majority of her work, she explains, starts not with the desire to tackle an overarching social theme but with a single spark – such as the incident with her son's friend – that illuminates something bigger. This has led to criticism that her plays are banal and middle of the road; that they're dependent on the interpretation of great actors for their success. But it has also brought her immense popularity; there is, among a handful of critics, the somewhat snobbish belief that her plays are for people who don't normally like going to the theatre.

Partly, Reza attributes her no-nonsense attitude to having initially trained as an actress. She studied at the renowned Jacques Lecoq school in Paris before turning professional for several years. She wrote her first play, Conversations After a Burial, in 1987 in her late 20s "because I was always writing anyway. I knew I was good at it" and has since written seven plays, five novels and one work of non-fiction.

Her experience on stage, she says, "informed my work enormously". Her American translator, David Ives, has said in the past: "Half the reason her plays get done is because actors want to do them… there's a crackling surface there for a performer."

She consciously makes things easy for the crew also. Her plays are all set within a single set, contain no more than four people and never include suggestions for a character's appearance or biography. "Because even if you say to an actor, 'This character was beaten up as a child', what can they do apart from say, 'OK' and then just get on with it?" Reza says. "It serves them nothing. Writing is a lot more organic than that. It's not at all intellectual."

By now, she is talking in a rapid stream of French and her bobbed hair – which I'm realising is a helpful barometer of her internal mood – is getting increasingly animated, springing up this way and that, so that Reza has to brush it out of her face. She stops herself, then laughs at her own intensity. "Well, for me, at least."

It is a curious thing, this laughter of hers because, according to almost every interview with Reza I have ever read, she is meant to be po-faced and pretentious, a woman quick to take offence, who is snippy and defensive in her responses. "Laughter," she said in one such interview in 2001, "is very dangerous."

And yet the petite woman sitting in front of me is all smiles, lightness and enthusiastic hand gestures. She seems to be the very opposite of theatrical pretension. When I describe her plays as accessible, she seizes on this and agrees. "Yes, definitely. I love this definition. I am OK with that. Complex ideas but made accessible. There's no point in writing theatre if it isn't accessible, because no one will see it. The greatest playwrights such as Shakespeare or Molière – to whom, by the way, I am not comparing myself – they were also accessible."

The quote about laughter being dangerous was, she says, taken out of context. And it seems self-evident that anyone who makes a character throw up on stage over a priceless Kokoschka catalogue in the middle of a supposedly civilised discussion between adults (as Annette does in God of Carnage) must have a sense of humour.

"In Art, there is a phrase about 'culture that I vomit over'. In God of Carnage, I put it literally: she vomits on a pile of art books." Reza grins, apparently enjoying the idea tremendously.

At no point does she scowl like the grande dame she is meant to be. She only allows me to pay the drinks bill after checking I will be reimbursed. When I comment on her watch, she takes it off to show it to me. She chats easily about her two children with film director Didier Martiny – a 23-year-old daughter, Alta, who is a criminal lawyer, and her son, Nathan, 19, who wants to be a singer. She could not be more charming.

Perhaps age has mellowed her. Perhaps it is that we are doing the interview in French so she feels more comfortable expressing herself. Perhaps she's just having a good day. Whatever the reason, there is no sign of the spiky harridan I had been expecting. How, I wonder, has this idea of Reza gained credence?

"I know!" she says, her limpid eyes widening in mock-horror. "I'm so frightened of the English. There was one article written that said something like, 'I hated her before; I hate her even more now I've met her.' I have been the recipient of some very disagreeable personal attacks and I don't understand why."

As a woman operating in the male-dominated world of theatre, she has never encountered obvious sexism but "in the first interviews I did, I was young. I didn't know any better and I used to take out my lipstick and put it on and I think that wasn't good at all. It was seen as too feminine… perhaps they didn't take me seriously".

Her success, too, one imagines, must stick in the craw of those who believe their writers should be penniless artists living in romantic garrets, grateful for any small sliver of attention they receive. "Perhaps, but I've never played that game. I don't consider myself a celebrity or an intellectual. I'm a writer and that's not the same… I don't want to have an opinion on current affairs, on politics and, in a way, that's bad for me because if you take the position of an intellectual, it gives you authority. But – too bad – I don't want to do it. I have pretension enough to think that writing should have its own authority."

She says she is wary of becoming "a spokesman" for her characters. "We ask writers to have a vision of the world, to take positions. I don't like to do that because I want to be able to write characters who have different takes on life and for them to be convincing."

Her avowedly apolitical stance makes it all the more bizarre that, in 2006, Reza chose to shadow the then French presidential candidate Nicolas Sarkozy for a year leading up to his election in May 2007. The book she wrote about this experience – L'aube, le soir ou la nuit (Dawn, Dusk or Night) – described Sarkozy as a pint-sized egoist driven by "a childlike search for approbation". In one chapter, Reza describes the future president grabbing a copy of Le Figaro "visibly gripped" by an item on the front page. It was not the news story about Iran or the French election that had captured his attention, but an advertisement for a luxury watch. "That's a nice Rolex," Sarkozy said.

What does Reza make of his time in office? "Nothing in particular," she answers, with almost wilful opacity. "The book was not at all political. It was an observation of a man, a movement… I can have an opinion about the way he runs the country but it is no more interesting than that of anyone else, of a normal citizen."

Unsurprisingly, given that her observations pulled no punches, she is no longer in contact with the president. "I didn't have the desire to create a link with him. When the book was done, it was evident to me we could never see each other again. Ours was not at all a friendly relationship. It was codified: I always had my notebook because for a writer, to be seen to have a cosy relationship with power is a bad thing. If tomorrow he was not president, I'd gladly have dinner with him."

I'm sure Sarkozy will be relieved to hear that.

Still, one imagines that Reza, herself the child of immigrants, must have some views on Sarkozy's approach to integration. In April last year, the president banned the wearing of the burqa in public places and later declared that he believed multiculturalism had "failed". At first, true to form, Reza refuses to comment on this but when I push her, she acknowledges that her parents, despite being foreigners, raised her with "the absolute idea that we must love France" and insisted she speak perfect French.

"I have a real sadness when I see the children of immigrants, the young people in the suburbs who were born in France but who don't speak the language at all well. They are choosing to marginalise themselves. This way of speaking in the suburbs is half-Arab, half-French and I don't understand it. It's a way of marking yourself out.

"It's not about keeping your accent – my mother still has her accent, she still gets 'le' and 'la' confused and it's charming – but it's the people who were born in France, who went to school here. My parents always said the only way to integrate was to speak the language perfectly. It's a politeness, a way of thanking the country that welcomes you, to become a vehicle for its language."

And maybe it is this self-confessed respect for language, this delight in its nuance and capacity for obfuscation, that gives Reza her ear for dialogue. Which makes it all the more interesting that her success relies, in large part, on her translators – playwright Christopher Hampton, who won an Oscar in 1989 for his adaptation of Dangerous Liaisons, has translated most of Reza's plays for the British stage. Did she find it difficult to trust him?

"Oh, but I don't trust him at all!" she says, joking. "No, I adore him, he's a great friend, but I'm not blindly trusting. I remember the first time we met, he had translated Art into English and I called him up and said, 'I received your first draft.' He said, 'What do you mean, my first draft? It's the play. It's the translation. It's not a draft.' I said, 'Yes it is. There's work to be done.'

"Up to that point, Christopher had only ever translated dead people. This was the first time he'd had someone alive, on the phone to him. We reworked and reworked it and I know I was annoying him and he was saying to people, 'She's giving me such a hard time and she barely speaks English!'" There is a pause. Then she adds: "Now my English is much better."

Her eyes are twinkling as she says this, but she's deadly serious. There's a core of steel underneath her vivacious exterior; a determination that belies her easy manner. As she finishes her tea and gives me one last, precise little smile, it seems that Reza, like her characters, has aspects of herself she would prefer to remain concealed.