Any revival of D.H. Lawrence’s tale of Lady Chatterley contends with years of mostly insipid notoriety. Long after the days of book bans, Lawrence’s work became a tattered hand-me-down symbol of dirtiness, then was further obscured by the gauzy lens of numerous soft-core screen renditions. In many minds only a simplified fantasy — a dainty aristocrat is swept away by a swarthy woodsman with callused but attentive hands — “Lady Chatterley” has nevertheless endured, a risible byword for bodice-ripping titillation.

“Lady Chatterley,” the award-winning new adaptation by French filmmaker Pascale Ferran, clears away all the rot and lets in the light. Working from an earlier, more intimate version of Lawrence’s work entitled “John Thomas and Lady Jane,” Ms. Ferran and especially her Chatterley, Marina Hands, infuse the film with an absorbing sensuality and a moving sense of equanimity. The yearning and connection experienced by the characters feel like life being restored, not a desperate escape from it.

Much of Ms. Ferran’s success lies in bringing the sentiments of Lawrence’s heady prose to a tender, human level. The book’s most torrid passages, after all, aren’t the sex scenes but the screeds decrying the ravages of the Industrial Revolution and man’s rude will. “Lady Chatterley” fervently embraces the story of a man and woman coming alive in love, without tethering their rustic communion to a greater didactic point.

The lady of an old manor house, the young, slim Constance Chatterley marks time and takes care of her crippled husband Clifford (Hippolyte Girardot). An embittered, impotent veteran of World War I, he manages the nearby coal mines that these days recharge the family fortune. Meanwhile, Connie slowly fades away, as if her spirit were emptying out. When her sister pays visit and is shocked by Connie’s pallor, she helps get Clifford a nurse so as to give Connie a chance to convalesce and, well, get out a little.

When Connie passes by the secluded cottage of Parkin, the gamekeeper (Jean-Louis Coulloc’h), an unexpected glimpse of him bathing shirtless knocks her flat. That simple sight, a sensual and aesthetic epiphany before a sexual one, reveals to her the possibility of desire and a new awareness of the body. Thanks to Ms. Hands’s extraordinarily expressive and alert performance, you can almost hear Connie’s head humming.

“Lady Chatterley” builds casually to the couple’s first tryst on the cottage floor, setting the leisurely flow that holds throughout the film’s elegantly wrought and vibrantly shot episodes. The lovers’ eager anticipation of each rendezvous deepens into a constant mindfulness of one another and soon enough into an abiding love, rarely as palpable onscreen as it is here.

One of the movie’s many unostentatious merits is its attention to Parkin as well as Connie. Mr. Coulloc’h, who looks like a stockier and less pretty Brando (mid-career and minus the Method), infuses Parkin with a reticent but keen sensibility. A prideful vulnerability emerges with particular poignancy when they take stock of the strength of their bond, and when Connie makes well-intentioned offers to buy him a farm to run.

The class-crossing couple’s serene scenes together make Connie’s time at the manor resemble return trips from a foreign land. Amusingly, the nurse, Mrs. Bolton (Hélène Alexandridis) susses out Lady Chatterley’s affair rather quickly. Clifford’s big scene stems from the humiliating results of using a sputtering motorized wheelchair in unsafe terrain, one way in which Ms. Ferran manages to reference Lawrence’s rhetoric about the living death of industrial and postwar life.

The depiction of sex is probably an unavoidable point of interest in a work with such a history of censorship. Yet the tender scenes of “Lady Chatterley” feel utterly natural, never falsely built up, nor mindlessly engaged. They’re a far cry from the usual activity — subtly moralizing, art-house diligent, or mass-produced — that flickers onscreen. But to single out the sex in “Lady Chatterley” would be to betray the film’s own rich, layered view of sexuality and life. Mature content indeed — the film feels uniquely hopeful, an exaltation of both body and soul.