And if the Louis we saw before the transplant was inscrutable, the Louis we see afterward is no one we quite recognize, either. Early in the picture, Louis kills a young man with a hunting knife, for no reason we can discern. Louis has a son, or a man whom we assume to be his son (played by Grégoire Colin), from whom he's mostly estranged. Louis seems gruff and unprincipled, and he also seems to have lived a life in which he's made a lot of money. (He pays for his new heart with stacks of bills procured from a safety-deposit box in a Swiss bank. The operation takes place somewhere in Asia, although it's not clear exactly where.)

But after the operation, we understand Louis less, not more: We see him arranging to buy a very large boat -- a ship, really -- for his son. But who, exactly, is his son? Does Louis have more than one son, or no son at all? He travels to Tahiti, a place where, we surmise, he lived long ago; he seems to believe that he'll find this possibly mythical son there.

Denis is a challenging director, as anyone who has seen her languorously vivid "Beau Travail" knows. She's also capable of showing warmth in unexpected ways, as in her one-night-stand reverie "Friday Night." (Both of those movies, like this one, were shot by Denis' longtime collaborator, Agn`s Godard, one of the unsung geniuses of modern cinematography.)

"The Intruder" is a colder movie than either of those two: It partly takes place in a winter forest, a mystery landscape dotted with snow-draped trees and also the occasional frozen corpse. But Denis isn't a cruel or arrogant filmmaker, out to make us feel stupid for wanting a story to cling to. The story is there -- it's simply that she's veiled portions of it from us, perhaps a way of pushing us toward trying to understand the characters through what their faces, and their bodies, tell us. We're never granted the certainty of knowing we're right, but that too, I think, is part of Denis' intention: We need to trust our perceptions even when there's no way of confirming them; it's the only way we can keep ourselves free and open enough to respond to any art.

Perhaps the oddest, most bracing characteristic of "The Intruder" is how sensual it is, although not in the ways we usually think of sensuality. The music, by Stuart A. Staples (of the band Tindersticks), is spare and vital to the point of being unsettling: Wrought from just three instruments -- guitar, trumpet and some sort of (possibly synthesized) organ -- it shivers over the surface of the images with unnerving immediacy. Whenever the music kicks in, a sense of dread creeps over the picture like a sinister vine.

You need music like that to stand up to Godard's visuals: The sight of Louis' naked back, his skin freckled from years of sun, or just from age; the way we see, in a sequence that cuts deep emotionally without violating our trust, the moment where Louis betrays his loyal dogs (who, I will note, go on to survive without him); a lingering shot of waves rippling through water, possibly the wake of a boat we're not allowed to see. And then, most potent of all, the movie's final vision: That of Béatrice Dalle -- who plays one of Louis' neighbors, a character who's just as mysterious as he is -- rushing through the icy landscape on a sled pulled by a team of muscular dogs. Dressed in her shaggy furs, with that nutty gap-toothed smile of hers, she's a crazy snow baby; there's something demonically sexual in her need to keep moving.

Even the sounds of "The Intruder" stick with you -- like the scraping, buzzing noise made by Louis' cordless electric shaver. (He's dressed in a suit and tie and feels the sudden need for a shave -- outdoors, no less.) You can explain some of those sounds and images in words, and others are maddeningly elusive. But the experience of assembling them requires that we put our senses to work completely; "The Intruder" never lets us coast.

So what, exactly, does "The Intruder" mean? Or, to put it more bluntly: What on earth is Denis going on about? She may be asking us to think about what we mean when we talk about "the heart." Do we mean merely the organ, or the very center of us? Denis freely mixes the metaphorical with the literal, wondering what might happen if our familiar, comfortable hearts, the ones we've had for years, the ones we're used to, were suddenly replaced by something foreign, something attuned to another person's rhythms, desires, anxieties -- the ultimate "intruder." If our bodies can reject organs, can they reject experiences, too? The answers to all of those questions are written between the frames of "The Intruder." You'll find them only between the beats.

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