Personal Shopper is the most interesting film in which the mysterious creature Kristen Stewart has appeared, and the oddest. Olivier Assayas cast her as a personal assistant to an actress in Clouds of Sils Maria three years ago. This time, he has her playing Maureen, an American girl in Paris whose job is to buy clothes and jewellery for a woman she loathes - a vapid German supermodel named Kyra, whom we never quite meet.

Maureen whizzes around Paris on her scooter, from Cartier to Gaultier to Chanel, selecting outfits for Kyra, who's never home. She is forbidden to try them on, but some of the staff use her as a mannequin, because she's the same size. Maureen hates this world - even though she has the kind of access some women dream of - because she is profoundly ill at ease.

Is there any actress better suited to those words? Stewart is the least cheerful actress on the big screen since Garbo. Stewart seems to battle the camera, rather than embrace it.

In this film, in a very fine performance, she seems to resist letting us see her eyes - the very organ that film actors most rely on. It's as if she is holding the world at bay, keeping herself hidden.

When Assayas - a skilled technician as well as a movie buff - moves in for a rare close-up, the impact is profound, beautiful. She so rarely lets us come this close, either to her beauty or what ails her.

With Assayas, she has a director who can build a structure around that void, which some people take as an absence of talent. It's not. If Assayas calls her the best actor of her generation, we may assume she has something special, beyond her chiselled beauty. It's also true that not many directors yet know how to use it, except in fairly monotonous "I'm so vulnerable" kind of roles.

That's present here too, but it's not the only thing. Maureen is a twin, and her brother Lewis has recently died, leaving her halfway to madness. They shared the same congenital heart condition so it was not a complete shock.

Lewis was a medium, a gift she does not feel she shares, but they made a pact. Whoever went first to the afterlife would send a signal back, somehow. So Maureen spends a long night alone in the dark in the country house that he shared with his artist wife, Lara (Sigrid Bouaziz).

This allows Assayas to dip into some horror movie conventions, although he does it semi-seriously. He's a meta kind of guy and a modernist, which might explain his attraction to Stewart's icy gifts.

The modernism here is about being alone in the age of the mobile phone. There's a long and fascinating sequence when Maureen goes to London for the day to pick up yet more expensive clothes. Someone texts her on the train - someone who knows a lot about where she is and what she's doing. Is it Lewis, she wonders?

We know there is another candidate - a man who might be trying to seduce her. She's not sure what she feels - sexual attraction feels better than grief. It's the kind of thing Hitchcock would be exploring if he were alive today, and it anchors the film's pitch to be taken seriously.

At Cannes last year, some critics refused it that honour, offering boos instead, but the jury gave Assayas the prize for best director. I'm with the jury.

It's a bit crackpot as drama, but Personal Shopper has such controlled burn, such depth of feeling around this topic of grief, and such an aching performance from Stewart, that it hardly matters that it doesn't quite make sense. Logic is over-rated.