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A woman is to be looked at, or so sayeth the world of men. You think that’s no longer true in the 21st century? Our movies and TV shows insist otherwise, as do our advertisements, fashion spreads, and billion-dollar hair and cosmetics industries. To look is to possess; to gaze is to own; to take a photograph or paint a portrait is an act of laying claim. None of this is news.

But what if the person looking is a woman? And what if the woman being looked at looks back? What happens if you take men out of the equation altogether? Who owns who, or does the notion of “ownership” fly out the castle window? These are some of the questions dramatized with stately but ravishing ardor in “Portrait of a Lady on Fire,” Céline Sciamma’s extraordinary fourth feature and a movie of body, heart, and mind.

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It’s the late 1700s on the windswept coast of northern France. A painter is rowed ashore to an isolated chateau, the cool and contained daughter of a renowned artist. She has been hired, in secret, by a duchess whose own daughter is unhappily engaged to be married and whose distant fiance wants to see what his future wife looks like. Could the painter befriend the girl and create a portrait without letting her know?

That’s the seed of plot from which “Portrait of a Lady on Fire” expands onscreen and in a viewer’s head. The painter, Marianne, is played with sober professionalism by Noémie Merlant; her rebellious subject, Héloïse, by Adèle Haenel. One is brown-eyed and dark, the other blond and blue-eyed; they could be each other’s negative. The mother (Valeria Golino of “Rain Man”) departs for the city, leaving the painter to her task, which is — what, exactly? Create a painting fit for a rich man’s gaze? Or see Héloïse as a friend, a companion, a human being not for viewing or sale?

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Luàna Bajrami (left) and Noémie Merlant in "Portrait of a Lady on Fire."
Luàna Bajrami (left) and Noémie Merlant in "Portrait of a Lady on Fire." Neon via AP

Sciamma is a formalist, and “Portrait of a Lady on Fire” moves coolly and steadily on its tracks. Claire Mathon’s camerawork is as exquisitely framed as Marianne herself might make it, each image following the next at the pace of a slowly quickening gavotte. Vivaldi’s “Four Seasons” is discussed and played on a harpsichord — the cloistered Héloïse has never heard a live orchestra — and that’s somehow fitting for a movie that feels composed rather than shot.

As the two women grow close, attended by a country maid, Sophie (Luàna Bajrami), who becomes a co-conspirator and the subject of her own drama, we wait for the moment when Marianne’s “friendship” is revealed to be an act. By the time that happens, of course, it has deepened into something rawer and more complex, in no small part because Héloïse is taking the painter’s measure as surely as Marianne is sizing up her subject. “Portrait of a Lady on Fire” ultimately turns profoundly sensual, but it’s also a movie of ideas; I don’t know that I’ve ever seen a film that works so well on both the emotional and intellectual levels.

Because there are no male characters to speak of, the casual appearance of a porter in the chateau’s kitchen late in the film becomes a momentous signal that the idyll may be nearing an end. Sciamma’s previous movie, “Girlhood” (2014), was about a group of African-French teenagers in modern-day Paris, and it’s clear the filmmaker is fascinated by the private worlds of women — who they are when men aren’t around, when they’re not being seen. The new film’s title derives from a spooky nighttime sequence in which the two women and the maid join a group of peasant women gathered around a bonfire, singing in harmonies that feel ancient and rough.

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Eventually Marianne has to put down her brush and participate rather than observe; eventually Héloïse has to come down off her podium and be more than the observed. “Portrait of a Lady on Fire” drifts into a love story that never once feels didactic but that rises instead from the heat of throwing away notions of subject and object entirely. Like so much in this unique film, the scenes that follow are both metaphorical and anything but.

On top of all this, Sciamma has given us a great movie about painting and process and the making of art. We watch Marianne build up the layers of her portrait and then start all over again, willing the spectral Héloïse she sees in her head onto the canvas. The last film to work its way so deeply into this subject was Jacques Rivette’s masterful “La Belle Noiseuse” (1991), in which aging painter Michel Piccoli tried to capture nude Emmanuelle Beart over four hours of movie while discoursing with her on subjects aesthetic and philosophical.

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“Portrait of a Lady on Fire” can be viewed as a heady retort to that wise male classic. Gently but firmly, it insists that looking is petty theft unless looks are exchanged — and that just when you think you’ve snared a woman in a frame you find you’ve caught nothing at all.

Adèle Haenel in "Portrait of a Lady on Fire."
Adèle Haenel in "Portrait of a Lady on Fire." Neon via AP

★★★★

PORTRAIT OF A LADY ON FIRE Written and directed by Céline Sciamma. Starring Noémie Merlant, Adèle Haenel, Luàna Bajrami, Valeria Golino. At Boston Common, Kendall Square, Coolidge Corner. In French with English subtitles. 121 minutes. R (some nudity and sexuality).



Ty Burr can be reached at ty.burr@globe.com. Follow him on Twitter @tyburr.