Some critics of Claire Denis's new film have complained that too much of the dream world makes it into the narrative, writes Donald Clarke.

Having as its core the story of a mysterious elderly man in search of a new heart, The Intruder drifts off from the Jura Mountains to Pusan in South Korea before settling enigmatically in Polynesia. The protagonist, played with dignified solidity by Michel Subor, may be the father of a young man who lives nearby with a Swiss border guard. Béatrice Dalle turns up as the animalistic Queen of the Northern Hemisphere. Excerpts of Subor's performance in Paul Gégauff's 1965 film Le Reflux are stirred into the stew. What on earth is going on?

"The number one question I am asked is, why is it so radical in its narration," Denis says, when we meet up at the Edinburgh Film Festival. "It's a little bit surprising, because I think it is clear that this is a mental journey going from north to south. I thought, if anything, it was a naive metaphor. The fact that dream and real cinema are mixed together in the central character I did not think of as radical."

In fact the universe of dreams has frequently made incursions into the French director's cinema. Beau Travail, her virtually wordless 1999 masterpiece, which relocated Herman Melville's Billy Budd to a foreign legion camp in Africa, forewent conventional action for a sleepy, sinister playing out of military rituals. Trouble Every Day, a film everyone apart from Denis saw as a high-brow horror shocker, was so relentlessly, absurdly revolting it was dismissed as a nightmare. Her last picture, Vendredi Soir, may, she has admitted, all have taken place in the mind of a commuter trapped in a traffic jam. If anything, it is reality that seems out of place in The Intruder.

At any rate, the director is in no mood to clarify the film's puzzling turns. A small intense woman, Denis, now 57 years old, enjoys - if she enjoys anything - wrapping up her enigmas in further mysteries. While failing to clarify exactly what is going on, she mentions that the picture, though inspired by philosopher Jean-Luc Nancy's musings on his own heart transplant, works as the story of Michel Subor's life. Subor, who is probably still best known as the star of Jean-Luc Godard's Le Petit Soldat, had retired from acting when Denis coaxed him back to take a supporting role in Beau Travail.

"I don't think I realised this until I saw the film on a big screen in Venice last year," she kind-of explains. "I realised there was something very strange. Michel told me: 'I think the character is transforming me.' And I looked at him and said: 'You are already so much the character. It is you.' " But he is also Johnny Cash. Yes. I gave Michel a lot of Johnny Cash albums. He was still alive then. I was showing Michel a lot of photos and documents of Johnny: 'This is the kind of selfish man the character is.' Because nothing was nice about Johnny apart from his wife. But of course you couldn't resist him. But I was not going to actually use the music. That would be too obvious." (No fear of our Claire being too obvious.)

None of this sniping is to deny The Intruder's bewitching power. Making captivating use of characteristically liquid photography from Agnés Godard, one of many regular collaborators, Denis finds interesting, disconcerting images to decorate every frame. And, as always, her way with sound is astonishing. Few other directors can communicate so much without the use of dialogue.

"I often have more dialogue in the script," she says. "Then I get on the set and decide not to use it. I am not joking when I say that I have not programmed myself to use so little dialogue. It is just something that happens."

Largely a stranger to humour, an enthusiast for wilful enigma, Denis could be put forward as an archetypal French art-house director. Yet a significant period of her apprenticeship was spent working in the United States.

Raised in Africa, where, far from any cinema, her mother used to talk her through the plots of favourite films, Claire Denis initially studied economics - "my father really wanted me to be a teacher" - before enrolling in film school. One of only three girls in a class of 20, she was talent-spotted by the great French director Jacques Rivette. Then, somehow or other, she found herself in America working as Wim Wenders's assistant director on the memorable 1984 road movie Paris, Texas. Sam Shepard's script evolved as the crew travelled through the west.

"It was great. I first met Wim in Portugal," she says. "Then I flew to Houston and we drove to Dallas in a van. We were travelling for two months or so on the road just listening to all that music. Every now and then he would go off to Arizona and meet with Sam Shepard and leave me in charge. I really learned a lot. A strange experience. I learned from Wim that this driving around is the best way of crystalising a film. I thought: we should be working, not driving. But he was working." She also learned how to produce luscious images on a limited budget.

Denis's debut feature, Chocolat, a considered working-through of incidents from her African youth, looked wonderful. Beau Travail and The Intruder, neither of which had significant budgets, are equally easy on the eye.

"I think I am sort of a dictator," she says with just a hint of a smile. "I would think again before shooting a film like The Intruder on this budget. But I was convinced we could do it. So every day I had to convince the crew that it could be done. The same with Beau Travail. Every day I have to tell the crew there is enough money."

Do we detect a sense of humour here? Some years ago I conducted a public interview with Denis, and was taken aback by how reluctant she was to laugh and how surprised she was if you discovered jokes in her work. The cannibalism in Trouble Every Day (a hoot, if you're in the mood) is, I suggested, surely a gag? Certainly not.

In her defence, she recognises that absence. In the 1980s she worked with the American director Jim Jarmusch and now concedes that his jokes confused her. Four of her films have been scored by Tindersticks or individual members of that preternaturally gloomy Nottingham band - The Intruder's soundtrack is credited to Stuart Staples, the group's lead singer - and Denis is still not sure when the boys are having her on.

"I think it is something to do with education in England and America," she muses. "The French sense of humour is very different. There we start laughing even before we have said the joke. Then I look at Stuart and he sounds exactly the same when he is being serious and not serious. I find it hard to understand."

She doesn't exactly smile when she says this. Those eagerly anticipating Claire Denis's first light comedy may be waiting some time.

The Intruder opens at the Irish Film Institute on Friday