“It’s been 20 years, dear. Don’t be jealous of a ghost.” So says filmmaker Ismael (Mathieu Amalric) to his lover, Sylvia (Charlotte Gainsbourg), in the new film Ismael’s Ghosts (Les Fantômes d’Ismaël) when asked if he “still thinks of” his late wife, Carlotta, who vanished without a trace two decades prior.

As it turns out, his brooding belle should have been jealous — we soon discover that (spoiler alert!), after being pronounced dead, said “ghost” (played by Marion Cotillard) was merely Caspering around another continent, coming back from the grave looking more Lady Dior than Annabel Lee. At first, Carlotta’s mirage-like appearance on a beach suggests she is but a figment of Sylvia’s fearful imagination. But given that Ismael’s Ghosts is an Arnaud Desplechin film, it’s worth remembering that anything is possible — and what often seems the least plausible is in fact what we’re going to get.

In person, the 57-year-old director is spry with an impish smile, reminiscent of a philosophy professor whose lectures err toward entertaining rather than cohesive. The same might be said of Ismael’s Ghosts, his latest feature, its US version a full 20 minutes longer than the cut that opened the Cannes Film Festival last year. An epic soufflé of a film, it is equal parts splendid and convoluted — and includes some of the hottest and most realistic hetero sex seen on the big screen in ages.

Title notwithstanding, and no matter Amalric’s raffish magic, the most resonant — and haunting — scenes in the film are those shared by the two women, every word and glance between them truly combustible. “You’re not that different,” Carlotta tells Sylvia, as they get to know each other during a very awkward tea for two. “You and I are the same.” To this, Sylvia warily agrees, white flag briefly raised at half-mast. On the surface, such a claim couldn’t feel more false. Where Sylvia is wiry and cerebral, a successful astrophysicist and supposed “prude,” Carlotta is a whimsical, willowy bohemian who dislikes books but has a soft spot for Rilke. But somehow they do seem the same insofar as they are fully, unabashedly themselves.

“I can’t say that when writing this film I wasn’t thinking, in the back of my head, of Marion Cotillard and Charlotte Gainsbourg,” Deplechin told me last fall at Lincoln Center after Ismael screened at the New York Film Festival. “They are two actresses that I really know and revere. Their art is so different. Both are very gutsy — they are both great artists — but their art does not come from the same place in their body.”

It’s admittedly hard to imagine two luminaries like Gainsbourg and Cotillard battling over such a troubled (if charming) paramour, but for the director this was just a pretext.

“My dream was to see these two women in the same frame on screen together,” Desplechin said. “I never thought about them as enemies—because it’s not two girls trying to date the same man. The situation is slightly more complicated. It’s absurd and tragic at the same time. So there is no villainy between them or bitterness between them. It is rather the confrontation between two women. There is no rivalry.”

Really? Despite the director’s earnest evaluation, the women seem instinctively to be in heated competition. Given how implausibly the film unfolds, it is understandable that the Guardian panned the film as “time-wasting silliness.” But for those with a tolerance — or appetite — for asynchronous tone and ecstatic leaps in logic, Ismael’s Ghosts offers a nuanced look at how women in mid-life grapple with fear and loneliness. When viewed through this lens, rather than as a film about a narcissistic filmmaker whose antics flirt with farce (at one point Ismael shoots his best friend in the arm during an intense bout of insomnia), a truth emerges in how each woman inspires the other to evolve.

“One great belief that I have is that we have a duty — each one of us — to reinvent ourselves. We have each day to try to reinvent ourselves,” Desplechin told me. “But you cannot do this alone. You have to meet someone. It could be an enemy, a friend, a lover — but we must always be taught by the people that we meet. A lot of people think we have to be firm, we have to stay the same. But, actually, we have to change!”

To witness characters come of age again in their 40s and 50s is regrettably rare, but Desplechin insists on a kind of all-consuming dynamism at any age, and at any cost. It is a testament to the film that both women eventually break from their initial types.

“You’re wondering how it ended?” Sylvia asks us in one of the film’s final scenes, breaking the fourth wall. As she details her husband’s denouement, you might begin to wonder if you even care what happened to Ismael. But, sitting face-to-face with this screen legend as she whispers, “Life has come to me,” it’s thrilling to think the same could suddenly happen to us.

Ismael’s Ghosts opens at New York City’s Quad Cinema (34 West 13th Street, Greenwich Village, Manhattan) on Friday, March 23, with a wider release to follow.