Though its story and its power turn on the possibility of the miraculous, writer-director Xavier Giannoli’s engrossing mystery The Apparition only dares implausibility in its initial setup. An 18-year-old woman in a village in southern France claims to have beheld the holy Virgin Mary herself, out on a rugged hillside. Young Anna (Galatea Bellugi), intense and charismatic in the manner of another teen French seer, reports that Mary has imparted to her a message calling for the building of a church and caring for the world’s poor. Pilgrims now flock to the site by the busload, much to the delight of the local priest (Patrick d’Assumcao) and a holy man savvy in marketing and media (Anatole Taubman), who have online prayer meetups to run and tchotchkes to peddle — after Anna has anointed them, of course.

Buying that’s no problem. What’s trickier: the Vatican’s decision to place a nonbeliever journalist in charge of the canonical investigation committee it dispatches to France to look into Anna’s claims. Weary and rumpled war reporter Jacques, played by The Measure of a Man’s weary and rumpled Vincent Lindon, perks up not long after accepting the curious assignment. By the end, he’ll be shouting at his team of bishop-selected experts, believers and skeptics, “I want facts, proof!”

Swallow the premise that this guy would be granted the authority of the Church, and The Apparition likely will please, intrigue and surprise, at least for its first 90 minutes or so. Jacques becomes fascinated first by questions of belief, then by Anna’s persuasive embodiment of conviction and at last by the oddities he uncovers. Why does a townsperson report having heard Anna scream right around the time of the purported appearance of Mary? And why does Anna collapse to her knees and tearfully beg him not to send off for testing a relic her parish has been displaying — a swatch of fabric smeared with what the locals insist is Mary’s own blood?

The scenes of investigation and pilgrimage have a disquieting power. Giannoli’s technique is direct and never mannered, his attention so attuned to the characters and their secrets that it’s a pleasant jolt when, almost incidentally, his camera settles on a vision: the archives beneath the Vatican, much more ordinary and ominous than Dan Brown has imagined; the wooded hills outside Anna’s town; the seer and some nuns at work pumping, via a machine, feathers into pillows. But the focus is on the people, on the faces of the stoical Jacques and the yearningly pious Anna.

She wants him to believe but also confesses to fearing what he’ll uncover; he wants to find the truth but soon comes to fear what it might do to her. The answers don’t quite satisfy, not that they could, and it botches the satirical elements involving the local parish’s efforts to profit off Anna — these clods are too transparently using her. In its back half, The Apparition wears on a while, tending to plot business not as engaging as its mysteries, but it’s admirably sober in its consideration of miracles, faith and potential charlatanism. Expect neither dramatic exorcisms nor those daft kill squads who forever are hunting down Dan Brown’s Robert Langdon.

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