“Insecure people are dangerous,” says Julianne Moore’s character in this movie. She should know. Todd Haynes has come to Cannes with this amusing and elegant drama, Highsmithian in its intimacy and malice; a darker shade of Haynes’s Carol, maybe? It’s an unacknowledged duel between two women, played by Moore and Natalie Portman, who have found a potent frenmity at an important stage in each of their lives. Periodically Haynes will present us their faces side-by-side in closeup as they gaze at themselves and each other in the mirror, Bergman-personae of wary malice.

Moore plays Gracie Atherton-Yoo, a controlling and neurotic woman in the familiar Moore style, who does in fact give us the traditional Moore self-pity crying scene. Gracie has hyphenated her surname with that of her much younger second husband Joe (Charles Melton); she has put her surname first. She lives in some style in the prosperous town of Calabasas, California, but it may be her husband’s income is paying for everything; all Gracie has is a hobbypreneur sideline baking fancy Martha Stewart-style cakes and selling them to the neighbours.

But Gracie and Joe’s marriage is founded on a sex scandal that once gripped the tabloids and disgusted and fascinated all America: she seduced Joe when he was just 13 years old and she was a married woman in her 30s. Grace got pregnant, went briefly to jail and is still on a sex offenders’ register. But their relationship survived and they have three children: two about to graduate high school and one at college. The children from her first marriage are the same age as Joe, the trickiest of whom is Georgie (Cory Michael Smith), a highly-strung personality who has been royally messed up by the whole business.

But everyone is excited by the news that Gracie’s life is to be portrayed in a sensitive independent movie – very different from the crass tabloid-TV re-enactments which we glimpse – and Gracie is to be played by Elizabeth Berry (Natalie Portman), a respected Juilliard-educated actor who wants to make a career move away from the silly television show about vets that’s made her famous. Gracie’s meta-doppelganger situation is comparable to that of Moore’s character in David Cronenberg’s Maps to the Stars, where she played a failing actress who gets a chance to play the lead in the remake of a movie that once starred her late mother.

Elizabeth shows up and hangs around with the starstruck family like their new best friend, asking personal questions of everyone to immerse herself in the part, trying to nail Gracie’s hairstyle, her mannerisms, her makeup and even her slight lisp. Elizabeth is going to redeem them all, and alchemically transform their notoriety and shame into celebrity like hers, because her portrayal will be sympathetic… won’t it? As Elizabeth gets closer to Joe, whose age she is, her Method preparation has given her a dizzying romantic closeness to this shy, attractive man and she senses that she can save him from a stagnant relationship with a woman who mommies and bullies him.

There are some flaws here: it is, for example, very strange that Elizabeth never asks Gracie about her spell in prison, as her jail scenes would surely be very important. But May December is delivered with a cool, shrewd precision by Todd Haynes, Julianne Moore carries off her dysfunctional queenliness very watchably and Natalie Portman has a great scene where she gives a lecture on acting to Gracie’s children’s high school drama class. She even talks about how sex scenes can gradually become authentically sexy for the participants: “Are you pretending to feel pleasure – or pretending not to feel pleasure?” Well, the pleasure is real here.

• May December screened at the Cannes film festival; it is released in UK cinemas on 17 November and on Sky Cinema from 8 December.