A throwback in both style and content, Sylvain Chomet’s follow-up to “The Triplets of Belleville” will appeal especially to filmgoers nostalgic for the movies of a half-century ago, but anybody willing to forgo the rapid-fire approach of most of today’s animated pictures should find this gentle, warmhearted fable a quiet charmer.

“The Illusionist” is based on an unproduced screenplay by Jacques Tati, the tall, rangy, nearly wordless French farceur who proved a unique screen presence in the five films he made between 1949 (“Jour de fete”) and 1971 (“Traffic”), and the design of the title character Monsieur Tatischeff is based on the man himself. (A cute insertion of a clip featuring Tati near the close certainly proves the point.)

Tatischeff is a down-on-his-heels magician of the 1950s who travels from one seedy theatre to another to perform with his chubby, obstreperous rabbit before unappreciative audiences. In Chomet’s adaptation, he travels from Paris to London for an engagement, but he’s totally upstaged there by a rock band called the Britoons and finds himself again unemployed. Happily an inebriated Scotsman catches his act and engages him to perform in a pub on a remote island in connection with the introduction of electricity.

There he encounters a naïve young servant girl whom he buys a pair of shoes. Believing that he can conjure up things at will, she decides to accompany him back to the mainland and he takes a paternal interest in her. They take up residence in a crumbling Edinburgh hotel that caters to impoverished vaudevillians—acrobats, a clown, a ventriloquist. And to provide food and the new clothes the girl expects, he takes on odd jobs, like doing his act in a department store window to attract customers. In time, however, she catches the eye of a handsome neighbor, and the illusionist decides he should bow out of her life in a bittersweet close.

Done in old-fashioned, hand-drawn 2D animation that mimics watercolor painting, the film looks delicious, with the characters set against evocative backgrounds. The pacing is—like that in Tati’s live-action films—decidedly unhurried, with plenty of time to watch Tatischeff as he wanders about, Tati-style. And there are lovingly choreographed sequences like those that Tati, in the silent-comedy mode he embraced, included in all his pictures. Chomet even makes room for an amusing animal figure in that rabbit, which causes all sorts of trouble and is instrumental in a finely worked-out scene in which the magician is served a stew by the girl and suspects the little fellow might be its main ingredient.

In other words, Chomet has managed to capture Tati’s own idiosyncratic comic approach, but in a fashion that seems more a channeling than an imitation. “The Illusionist” has the soulful, Buster Keaton-esque tone that Tati always aimed for, along with the slow-burning sight gags he specialized in.

The result is almost like having Tati back with us, and anyone who remembers what he was like in the flesh will appreciate that. Newcomers, meanwhile, have the pleasure of discovery.