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With more than 70 theatrical works and a handful of screenplays to his credit, Israel Horovitz knows a thing or two about building a script. That’s evident in his film directorial debut, “My Old Lady,” based on his 2002 play.

It’s the work of a man immersed in the stage. Although the film is capably made, its roots in the theater are clear — there’s lots to enjoy, but it has a slightly old-school, musty feeling about it.

The central figure, Mathias (Kevin Kline), a rumpled American in his late 50s, is newly arrived in Paris. He’s dead broke and plans to sell the large, well-situated apartment he has just inherited from his father. But there’s a problem (actually, two of them).

French law permits a real-estate agreement called a “viager,” in which a seller is allowed to remain in his or her house or apartment for life, in exchange for a lump sum and regular payments from the buyer. It can pay off handsomely for the buyer, but it’s a gamble.

Entering the apartment, Mathias is dismayed to find an elderly woman, Mathilde (Maggie Smith), in residence, and she has bad news — she’s in “his” apartment under a “viager” contract. She’s reasonably polite but firm, insisting on the tidy monthly fee that’s due her.

But it’s not just the old lady. Her adult daughter, Chloe (Kristin Scott Thomas), a teacher of English, also lives there and takes an intense dislike to the American.

This is a classic setup for comedy, and that’s what we get early in the film, particularly in the exchanges between Mathias and the old lady.

There are warnings — including Mathias’ despairing streak — that the story will take a darker turn, which it does. To avoid spoilers, I’ll just say we are made aware of heavy-duty family secrets and come to see that long-ago events can exact a deep, lasting toll.

The three veteran actors are a joy to watch, especially Kline, and Horovitz opens up the proceedings by treating us to many handsome street scenes. He has described the film as “a love letter to Paris.”

“My Old Lady” is affecting, even if many of the revelations and high-voltage speeches occur at predictable moments. But if you can look past this formulaic side, it’s a movie worth seeing.