Despite being “opened up” in Paris locations, Israel Horovitz’s screen adaptation of his 2002 play doesn’t entirely escape staginess—there are lots of two-person dialogue scenes, not to mention quite a few monologues. But thanks to the efforts of a superlative cast, the slight piece comes across as a charming mixture of comedy and drama.

Kevin Kline delivers an impressive mix of drawing-room humor and pain-ridden fury as Mathias Gold, a broke American writer who comes to the French capital to claim his only significant inheritance from his recently deceased, long estranged father: a large apartment, with garden, in an attractive part of the city. But he’s surprised to find someone living there: nonagenarian Mathilde Girard (Maggie Smith), an expatriate Englishwoman whose husband sold the place to Gold’s father in 1943. But the purchase was a viager—an archaic reverse annuity agreement according to which not only is the former owner entitled to remain in the property until death, but the new owner must pay that person an annual stipend. The upshot is that not only cannot Mathias sell the flat—which was his original intention—but he owes Madame Girard a monthly payment.

Learning of Gold’s straitened circumstances, Mathilde offers to let him stay in one of the upstairs rooms she no longer uses (though she takes his watch as a rental payment). But his presence immediately attracts the ire of her daughter Chloe (Kristen Scott Thomas), who also lives there. Mathias tries to make ends meet by surreptitiously selling of some of the furniture and negotiating with a sympathetic realtor (Dominique Pinon) to find a buyer for the place—which isn’t difficult to do, since an entrepreneurial builder (Stephane Freiss) has been trying to gobble up the entire neighborhood. But of course everything depends on how long Madame Girard will live.

Needless to say, the proximity between Gold and Chloe will lead to an emotional connection that neither of them initially desires. And matters grow even more complicated when Mathias discovers that his father’s relationship with Mathilde was something more than that of buyer and seller. The revelations will lead Gold to fall off the wagon, imbibing increasingly large quantities of wine from Girard’s apparently well-stocked cellar, and giving himself over to impromptu rants in positively Shakespearean cadences.

It isn’t at all difficult to predict where this is headed, and the mixture of near-farce and heavy-duty melodrama doesn’t always gel. But there are grace notes throughout, not only in Gold’s dickering with the reliable Pinon’s realtor, but in throwaway moments like a sequence in which Mathias encounters an opera singer (Sophie Touitou) warbling half of a duet from Mozart’s “Don Giovanni” on the bank of the Seine and joins in with the Don’s responses. Kline clearly relishes the range his role offers, and plays it big throughout. Smith is more subdued than she’s often been of late in programs like “Downton Abbey,” but she puts an unmistakable twinkle in Mathilde’s eye, and has no difficulty at all transitioning to the more serious moments. Thomas brings her customary gentility to Chloe, but it’s the most weakly written of the three leads, with a subplot about an affair with a married man that lacks the intended poignancy. Visually the picture is a pleasure, with cinematographer Michel Amathieu’s widescreen images looking great in both the interiors and exteriors, and production designer Pierre-Francois Limbosch’s settings possessing the proper appearance of slightly musty elegance.

The contrivances of Horovitz’s plot may have you thinking how much better the classic playwrights constructed this sort of thing, and one can certainly that the film might have been more imaginatively staged had an experienced director been at the helm. But his script offers both Kline and Smith some delicious lines, and they savor them for all they’re worth. “My Old Lady” may be creaky at times, but in the end it wins you over.