The sultry 1969 hit single Je T’aime … Moi Non Plus was a four-and-a-half-minute distillation of languid Gallic cool, in which a Frenchman, his voice coarsened by Gitanes, is heard billing and cooing with an ecstatically sighing young Englishwoman over the swirling motif of a baroque organ. That man was Serge Gainsbourg; his companion was Jane Birkin, the actor and singer, who has died aged 76. Though Birkin worked with some of the world’s finest film-makers, including Jacques Rivette and Agnès Varda, she knew that Je T’aime … would be remembered above everything else she did. “When I die, that’ll be the tune they play, as I go out feet first,” she said.

Birkin was 21 when she and Gainsbourg met while starring together in the film Slogan (1969). He was 40, and had previously recorded Je T’aime … as a duet with Brigitte Bardot, only for the actor to withdraw permission for it to be released. Birkin had already starred in a 1965 musical, Passion Flower Hotel, scored by John Barry, whom she married that year at the age of 19 and from whom she was divorced in 1968; he was the father of Kate, the first of Birkin’s three daughters. But it was on the duet with Gainsbourg, she said, that for the first time “somebody thought I had a pretty voice”.

She sang her part an octave higher than Bardot. “It gave it a choirboy side that [Gainsbourg] liked a lot,” she said. Rumours that the vocal track was recorded under the covers during a moment of intimacy were untrue (the couple were standing at separate microphones in a studio in central London) though they did nothing to harm the mythology surrounding a song that was later condemned by the Vatican. “I just remember thinking it was all terribly funny,” she said.

Among the countries that refused to give the song airplay was Britain, where it became the first banned single to reach the top of the charts, as well as the first non-English-language No 1. It was also the lead track on the 1969 album Jane Birkin/Serge Gainsbourg.

Birkin’s life remained inextricably linked to his. They were together for 11 years, and had a daughter, Charlotte, who became a successful singer and actor. Even after they separated in 1980, he continued to write for her, and she went on performing his songs for the rest of her life.

Far from being an adjunct to Gainsbourg’s legend, she possessed her own style, intelligence and attitude. Her wistful beauty was rendered unorthodox by an eager, gap-toothed smile. Her voice was as bewitching as her face: though she lived in France from 1969 onwards, and spoke French fluently, she never shed her breathy, crisply English accent.

She was born in London to Judy Campbell, an actor who had been a muse to Noël Coward, and David Birkin, who was a lieutenant commander in the Royal Navy and a spy during the second world war. His duties included taking British spies across the Channel to France and bringing back stranded airmen and escaped prisoners of war.

Jane was educated at Upper Chine school on the Isle of Wight. At 17 she starred with Ralph Richardson in Graham Greene’s play Carving a Statue; Greene himself had a hand in casting her. Her screen acting career began with a walk-on part in The Knack … and How to Get It (1965) and a controversial nude scene in Michelangelo Antonioni’s Blow-Up, which she agreed to because Barry had told her she wouldn’t dare.

She had a small role in the Warren Beatty caper Kaleidoscope (also 1966), played a model called Penny Lane in the psychedelic curiosity Wonderwall (1968) and starred with Romy Schneider and Alain Delon in the psychological thriller La Piscine (1969). She got on famously with Bardot when they starred together in Don Juan, or If Don Juan Were a Woman (1973). Gainsbourg directed her in a 1976 film named after their hit song; he cast her as a boyish woman who attracts the attentions of a gay man, played by the Warhol regular Joe Dallesandro.

Birkin was tremendous fun in two star-studded Agatha Christie thrillers, Death on the Nile (1978) and Evil Under the Sun (1982). In the cryptic Love on the Ground (1984), Rivette cast her and Geraldine Chaplin as actors drawn into a playwright’s mysterious world. She appeared in two films, The Pirate (1984) and Comedy! (1987), made by her then partner, Jacques Doillon, with whom she had her third daughter, Lou, also a singer and actor. Jean-Luc Godard directed her in Keep Your Right Up (also 1987), while for Varda she played a woman besotted with a 14-year-old boy in Kung-Fu Master! (1988); the film co-starred Charlotte and featured Lou, and was inspired by an idea by Birkin herself.

In the same year, Varda made her the subject of Jane B For Agnès V, in which the actor performed a variety of specially scripted scenes (in one, she was a Stan Laurel type, in another a cockney mother) interspersed with musings on her life. She received the documentary treatment once again when her daughter directed Jane By Charlotte (2021).

Her two most impressive performances came in Bertrand Tavernier’s These Foolish Things, aka Daddy Nostalgie (1990), in which she was moving as a woman trying to repair her relationship with her dying father (Dirk Bogarde); and La Belle Noiseuse (1991), Rivette’s spellbinding four-hour study of a painter (Michel Piccoli) and his new muse (Emmanuelle Béart), in which Birkin played the artist’s wife and former model, who must deal with the indignity of having her younger self literally painted over.

Later films included Alain Resnais’s musical On Connaît la Chanson (1997) and the Merchant-Ivory coming-of-age story A Soldier’s Daughter Never Cries (1998).

In 2002 Birkin was diagnosed with leukaemia, but by 2006 she had made her directorial debut with the autobiographical family drama Boxes, which she also wrote and starred in, along with Chaplin, Piccoli, John Hurt and her daughter Lou. She appeared in Rivette’s final film, Around a Small Mountain (2009), played herself in Hong Sang-soo’s Nobody’s Daughter Haewon, and was reunited with Tavernier for his comedy The French Minister (also 2013).

Her look had been widely applauded in the 1960s, and seemed never to go out of date. In the 80s Hermès introduced a large and exorbitantly priced leather bag, named “the Birkin” in her honour. Fashion journalists in recent years could still be heard celebrating the “Jane Birkin top”, referring to the white lace dress made famous by her in the late 60s. “Real life was what I was best at,” she told Vogue magazine in 2016. “I didn’t have confidence in movie cameras or on stage. But I did have confidence in what I wanted in real life. If I wanted to be barefoot and wear a mackintosh, I would do it. I didn’t give a hoot.”

It was at 40 that she finally discarded her youthful ingénue image and performed her first live concert: “I cut my hair off like a boy, I wore men’s clothes. I only wanted people to hear the music and words. It was fantastic. And it was so frightening. Serge was there and he kept lighting his cigarette lighter to make everybody put their lighters on.” That show was preserved on her 1987 album, Jane Birkin au Bataclan. She continued singing and recording into her old age; among her later albums is Birkin/Gainsbourg: Le Symphonique, from 2017, in which the couple’s songs received new orchestral arrangements.

In 2020 she published Munkey Diaries 1957-1982, containing diary entries addressed to her favourite cuddly toy from childhood, which she can be seen clutching on the cover of Gainsbourg’s 1971 album Histoire de Melody Nelson. She buried the toy with him after his death in 1991.

She is survived by Charlotte and Lou, and six grandchildren, and by her brother, Andrew, and sister, Linda. Kate, a photographer, died in 2013.

• Jane Mallory Birkin, actor and singer, born 14 December 1946; died 16 July 2023