French police detective Jules Maigret (“commissioner” is his title, but not in the American “Commissioner Gordon” sense) is back on television in the surprising but ultimately persuasive person of Rowan Atkinson, better known to the world as Mr. Bean.

The two-episode first season — “Maigret Sets a Trap” and “Maigret’s Dead Man,” each in the 90-minute “TV movie” form now favored for British mysteries — arrived here last week via the BBC and ITV-owned streaming service, Britbox. (A second season has also already aired in the UK.)

I have been waiting for these adaptations since Atkinson mentioned he was making them in the course of an interview three years ago. (“Mr. Bean” was having a 25th anniversary.) The creation of super-prolific French novelist Georges Simenon, Maigret may be my favorite fictional sleuth, after Jim Rockford and Elliott Gould’s Philip Marlowe. That he is based in Paris and that my French is just good enough to manage reading them in the original without running to a dictionary every five seconds may have something to do with this preference; but I like the chief inspector’s reflective ordinariness, his curiosity about people, his lack of melodrama; he is a soft-boiled detective.

There have been many Maigrets, in several languages, since the character first stepped onto the page in 1931, and each has found his own way into the character. French Maigrets include the great Jean Gabin, who played him on the big screen in the late 1950s and early ‘60s, Jean Richard (1967-1990) and Bruno Cremer (1991-2005).

Michael Gambon was the last English-language Maigret, in 1992 and 1993, between his work in “The Singing Detective” and becoming Dumbledore. (Richard Harris, who preceded him in that “Harry Potter” part, also played Maigret in a 1988 TV movie — as a sort of Irish Columbo, from what I can make out — a performance that created no fond memories among fans of the inspector.) Britbox is also showing both seasons of the Gambon series, which includes its own adaptation of “Maigret Sets a Trap” for instructive comparison.

The new adaptations are by Stewart Harcourt, who wrote some of the later David Suchet “Poirot” movies, “Miss Marple” episodes for both Julia McKenzie and Geraldine McEwen and half of Ashley Jensen’s “Agatha Raisin” series. Both episodes put the chief inspector into the heart of the story: In “Maigret Sets a Trap,” he has been unable to stop a serial killer; “Maigret’s Dead Man” finds him on a personal quest to discover the identity of a corpse, at one point (departing from the text) posing with Madame Maigret (Lucy Cohu) as proprietors of a quayside cafe to discover his killer. (This makes no sense, given that all Paris seems to know him, but c’est la tele.)

They are essentially true to the novels, if necessarily streamlined. At the same time, some scenes that happen offstage in the book are brought onstage for the series.

As in the Gambon series — the first “period” adaptation — Budapest, dressed with tricolor flags, cafe tables and French signs and sandwich boards, stands in reasonably well for midcentury Paris. Close viewers will note posters for Max Ophuls’ film “Lola Montes,” released in 1955, the very year “Maigret Sets a Trap” was published; a few may recognize the re-creation of Janine Niepce’s 1952 photograph of her father reading “Tintin” to her son in a park. Izis Bidermanas’ contemporary picture of a man walking a cat also seems to have been in the production designer’s scrapbook.

Atkinson’s Maigret likewise is largely in the spirit of Gambon’s — quiet and gentle, though not as playful; more cerebral, but not unfeeling. He has the pipe, of course — all Maigrets must — but not his habit of ordering or accepting a drink at every bar he enters.

Unlike Gambon, Atkinson is most famous as a funnyman, his rubbery face amusing even in repose. Casting him in this straight role is akin to casting Harpo Marx as Sam Spade (a thing I would watch, admittedly), and one waits almost nervously for the star’s first curled lip or popped consonant.

They do not come. As an apparent countermeasure, Atkinson turns in an especially contained performance, almost as if he were balancing the character on his head, careful not to let it fall and shatter — and get a laugh in the process.

Most opportunities for humor Atkinson lets go by; it’s a feature of his performance, not a bug, and it works, producing a new, sadder, but no less able Maigret, conscious of the fragility of things. (Shaun Dingwall provides sturdy, earthy contrasting support as Inspector Janvier.) Well, death is sad, and that’s the business he’s in.