Morin's sly, implacable arguments in favor of belief, his physical grace, and his material poverty all create an unacknowledgeable erotic nimbus around him. This causes Barny, who resists seeing her physical attraction plainly, to question her avowed atheism. She channels her sensual impulses into misguided longing for spiritual clarity.
One could almost impute utter cynicism to Melville, himself a Jewish atheist, for devoting quite so much of this movie to religious disputation; given that other, arguably more important things are elided or shown obliquely, the freighted dialogues between Morin and Barny seem incidental to what's actually passing between them. But that's really the point: Melville shows us an extreme distortion of feelings produced by Barny's loneliness and Morin's immutable vow of chastity. Implicitly, the church and the war both impose a drastic curtailment of existential freedom; Melville is depicting a world where natural impulse and the choice it presents are preempted by contingency, transpersonal exchange weighted and warped by external circumstance. This isn't to say that Morin ever exhibits desire. His interiority is hidden from his spiritual clients. If his baldly flirtatious manner indicates conscious seductiveness, it's unclear whether he's content to lure women into the arms of Christ or secretly wishes he could nail them.
...given how much of the movie represents Barny's point of view, we tend to see Morin as she does---as a manipulative male with markedly adolescent tics, really, who foists his libidinal blockage onto other people. If Barny never articulates this insight, it's there in Belmondo's gestures and expressions, his habit of running hot and cold in blinking alteration.