Daphne Du Maurier, the noted and quite popular British novelist, wrote genre fiction that has been translated to the screen several times over the years. Alfred Hitchcock adapted “Rebecca,” and earned the Best Picture Oscar in 1940 (and later put his stamp on another Du Maurier story, “The Birds,” in 1963). Nicolas Roeg, 33 years later, turned “Don’t Look Now” into yet another cinematic classic.

Du Maurier’s signature work, due to its highly calibrated mix of mystery, drama, and romance, opens itself up to repeated explorations. “Rebecca,” for instance, has been brought to the big screen, refitted to television, as both a television movie and a mini-series, and even converted into a play—once by Du Maurier herself).

And now, writer-director Roger Michell (“Venus”) tries his hand with “My Cousin Rachel,” which already has a celebrated 1952 iteration from director Henry Koster, featuring Olivia de Havilland as Rachel Ashley, an enigmatic woman suspected of murder, with Richard Burton as Philip Ashley, an eager young man who seeks to prove her guilt while protecting his estate, before succumbing to her charms. Burton landed a Best Supporting Actor Academy Award nomination for his performance and de Havilland garnered a Golden Globe nomination for Best Actress.

With such big shoes to fill, Michell wisely shifts the focus even more squarely on the character of Rachel Ashley, played by Rachel Weisz. (By the time of the earlier adaptation, de Havilland was already a two-time Academy Award winner: Best Actress for “To Each His Own” in 1947 and three years later in “The Heiress” and a celebrated screen presence, engaged in a rivalry of sorts with her sister Joan Fontaine, who beat her out for Best Actress in the 1941 race in “Suspicion”).

Weisz, a formidable actress in the modern era, with an Academy Award of her own at this point (Best Supporting Actress for “The Constant Gardener”), sets up a strong parallel to de Havilland. In times when female performers struggle to find challenging roles befitting their talents and aspirations, Weisz, like de Havilland before her, has sought to find complex characters. That is not to say that she has forgone opportunities in franchise efforts—like her two appearances in the Brendan Fraser “Mummy” series or the Matt Damon-free “The Bourne Legacy”—but she has tried to marshal her considerable charms in the service of drilling beneath the surface.

The highest praise I can offer is that Weisz, no matter the role, always projects a teeming intelligence, a sense that, in any given moment, there is much more going on inside the head of her character—behind the eyes—than might have been on the page of the script. And that is what makes her such a suitable fit as Rachel Ashley. In Michell’s film, we don’t even get to lay eyes on the character until almost 30 minutes into the story. We learn about her through the letters the older cousin, Ambrose, sends to his younger cousin and ward, Philip (here played by a decidedly twitchy Sam Claflin). There are hints that she might be Italian (blessed with a dark and impetuous spirit) and that she has voracious appetites—with all that might imply.

When she finally makes her grand entrance, Weisz embodies all of these possibilities and much more without an overly dramatic or naked display. The hints and teases come from Weisz’s eyes: sometimes cold and calculating and, in other moments, wounded and full of longing. Her Rachel is most definitely a woman of her times, constrained by social realities, but desirous of the ability to command her own destiny.

As we watch everyone react to Rachel, we get the sense that Michell’s adaptation is a bit unsteady, in terms of how the potential duplicity in Rachel’s nature is supposed to play out, but Weisz never wavers. There are no wild swings of emotion or plot-driven reversals in her approach to the character. As long as the focus is on Weisz, “My Cousin Rachel” is real and satisfying curiosity on today’s film landscape, a performance-fueled work anchored by a strong female lead who knows and remains true to herself.