Director Anne Fontaine tells a very dark fact-based tale in “The Innocents” in a style that seems a touch too beautiful and sensitive for the film’s good. The picture almost demands comparison with Pawel Pawlikowski’s “Ida,” and suffers from it; but while pulling its punches, it nevertheless survives even a coda that comes across as far too sunny.

The screenplay is loosely based on an incident that occurred in Poland late in 1945. Mathilde (Lou De Laage) is a French nurse working with a Red Cross team to tend to wounded French soldiers there. She is approached one day by Sister Maria (Agata Buzek), a member of a secluded nearby convent, who begs her for help. One of the members of the cloistered community is pregnant and in the throes of a long and painful delivery; she needs medical attention. Although forbidden to offer treatment to any of the locals, Mathilde nonetheless goes and delivers the infant by C-section. The Mother Superior (Agata Kulesza) is initially furious that Maria exceeded her authority by going outside the cloister and fetching Mathilde, but she agrees to take responsibility for seeing to it that the child finds a home in the area.

How the pregnancy occurred is initially not discussed, but soon the answer is revealed. During their occupation of the area, Soviet soldiers broke into the convent and raped seven of the nuns. Six more are still expecting, and after prodding from Maria, Mother Superior accedes to the French woman’s returning to care for the prospective mothers. But secrecy is essential: the nuns insist that if word of what had happened to them reached the community, the shame would be too great for the convent to survive. Even some of the pregnant women fear damnation for what has happened to them.

So the nurse becomes a regular visitor, creating a bond with some of the sisters (one giggling at her ministrations, another shrieking in terror)—particularly Maria, who entered the order late with experience of the world—and helping to deliver the babies, whom Mother Superior takes responsibility for placing with local families. She also helps to prevent an assault on the nuns by another Russian squad, which she frightens away by announcing that the convent is experiencing a typhoid outbreak.

This kernel of the narrative is powerful and, despite an arguable excess of gloss and artiness in Caroline Champetier’s widescreen images, which drain most of the color from the compositions, intense. But there are problems. One might object to a general feeling of delicacy in presenting the medical realities, either in the Red Cross hospital or the convent. A scene in which Mathilde herself is nearly raped by a group of Russian soldiers on the road, while quite potently staged, is a rather obvious dramatic means of expressing the character’s identification with the women she’s tending. And a coda in which Mathilde comes up with a plan that allows the convent to maintain its reputation for chastity comes across as too easy, especially after a truly ghastly revelation involving Mother Superior.

It can also be argued that the film simply tries to do too much. Not content with depicting the central story, it adds an overlay of theological issues, with Mathilde coming up against a kind of religious faith that she, as a typically secular French citizen, cannot really understand. And the addition of a fourth major character—Mathilde’s superior, a Jewish doctor named Samuel (Vincent Macaigne)—seems an obvious means not only of raising the issue of Polish complicity in the Holocaust, but of providing a quasi-romantic interest for the leading lady.

Nonetheless the tale at the center of “The Innocents” remains intriguing enough to make the film worth seeking out. De Laage might be treated too much like a typical heroine—she’s sometimes shot as though she were appearing in a 1950s Hollywood melodrama—but the performance itself is excellent, and Buzek is admirably restrained yet effective. Kulesza, who made such a strong impression as the sharp-tongued, cynical ex-official in “Ida,” has a less showy role here, But she certainly brings a high degree of implacable control to the Mother Superior. The physical production is solid, with the crisp, snowy locations lending a chill that’s entirely appropriate to the narrative.

“The Innocents”—which was briefly retitled “Agnus Dei” until wiser heads prevailed—is a flawed telling of a fascinating story, but the central subject is sufficiently compelling to overcome the miscalculations.