The distributor is playing a juicy joke on American audiences by releasing François Ozon’s “Double Lover” on Valentine’s Day. The twisted tale of dark, duplicitous romance, a kind of thriller loosely based on a novel that Joyce Carol Oates published under the pseudonym of Rosamond Smith, earns comparison to Brian De Palma’s early homages to the work of Alfred Hitchcock. In this case, though, Ozon’s model is the David Cronenberg of “Dead Ringers,” which was certainly one of the great anti-date films of all time, though in fashioning his adaptation he uses many of De Palma’s virtuoso tricks—split screens, mirrors and such, all of which fit into the doubling theme.

Twins born and unborn are the chief figures in the picture, which begins with troubled Chloë (Marine Vacth), who suffers from persistent stomach pain, visiting her doctor and announcing that she now feels ready to seek psychological counseling. She’s directed to Paul Meyer (Jérémie Renier), an analyst whose quiet, patient manner offers her comfort.

As their sessions continue, however, her impact on him grows so strong that he feels he can no longer treat her, preferring instead to become her lover. She and her cat Milo move in with him, and she gets a job as a guard—or people-watcher—in a typically chilly modern art museum. Eventually Paul will ask her to marry him.

Riding the bus home one day, though, Chloë has a shock when she sees a man who looks exactly like Paul conversing with a woman on the street. After setting aside the original presumption that Paul might be cheating on her, she tracks down the man—Louis Delord. He’s another psychologist, whom she now visits as a patient, keeping that a secret from Paul. His methods are far different from her husband’s—brusque, humiliating, domineering, even degrading.

Before long, however, Chloë learns that Louis isn’t merely Paul’s double—he’s Paul’s long-estranged brother. She tries to get Paul to admit that, but he doesn’t, and so she begins to investigate on her own, rifling through his private things and eventually looking up his onetime college sweetheart Sandra (Fanny Sage), from whose mother (Jacqueline Bisset) she learns what drove the brothers apart.

Meanwhile Chloë has entered into a steamy, often violent affair with Louis, who goes to incredible lengths to challenge her relationship with Paul. She begins harboring hallucinatory fantasies about having sex with both brothers simultaneously—in one case morphing into a Siamese twin herself—and imagining the brothers gamboling about as children (Keisley and Tchuz Gauthier). There is talk of “cannibal” or “parasitic” or “vanishing” twins, and by the close it has become a question whether Chloë’s psychological problems might not stem from something in her own life that even she is unaware of.

The real “double lover” here is Ozon, who obviously relishes presenting Paul and Louis as mirror images of each other, but goes far further than that, using other members of the cast in double roles in ways that point to what the ultimate “solution” to the underlying mystery is. He also offers a neighbor named Rosa (Myriam Boyer) whose weird behavior suggests she might turn on a dime from solicitous to dangerous, as well as lots of imagery involving felines—not merely Milo, but Louis’ cat (the genetic profile of which, again based on twins, he happily explains), not to mention the stuffed pets that strange Rosa keeps in her apartment.

It cannot be said that “Double Lover” makes a great deal of logical sense—neither did De Palma or Cronenberg’s films, after all. But like them it has style aplenty, as well as a dreamily enigmatic vibe and a sly mixture of playful sexuality and mordant humor. It boasts a crystalline production design (by Sylvie Olive), lustrous cinematography (by Manu Dacosse), clever editing (by Laure Gardette) and a score (by Philippe Rombi) that mimics the narrative twists, as well as performances that fulfill Ozon’s vision without a false step. Vacth makes an appropriately lovely and confused protagonist, and though Renier might not quite match the creepy perfection of Jeremy Irons’ turn as the Mantle brothers (one allusion to some perverted surgical tools obviously refers to them), he manages to give Paul and Louis distinct personalities. The supporting cast is small but exceptional, with Bisset assuming important dual roles that deepen the mystery of Chloë and Boyer practically stealing her scenes as the unsettling Rosa.

This might not be Ozon’s best film, but it’s a beautifully crafted example of his ability to evoke the slippery, ever-changing dimensions of human experience. One might note that it’s produced by brothers Eric and Nicolas Altmayer; but they’re not twins.