Actress Louise Brooks led a fascinating life, worthy of a biographical film, but she’s actually a peripheral character in Michael Engler’s “The Chaperone,” adapted by “Downton Abbey” creator Julian Fellowes from a 2012 novel by Laura Moriarty. Made by a variety of production companies including Masterpiece and distributed by PBS, it represents the sort of solid if somewhat stolid period drama that’s a mainstay of public television, though whether that will attract many small-screen viewers to theatres is a doubtful proposition.

The narrative begins in Wichita, Kansas, in 1922, when well-to-do local arts patrons Alan and Norma Carlisle (Campbell Scott and Elizabeth McGovern) attend a recital given by fifteen-year old dancer Louise (Haley Lu Richardson). The quiet, recessive Norma reacts to an announcement from Mrs. Brooks (Victoria Hill) that she needs a chaperone to accompany Louise to New York, where she’s been invited to audition for a position at the Denishawn Dance School of Modern Dance, and spontaneously applies for the position, to the distress of her husband, a prominent lawyer. As the sole applicant, she’s hired.

After an eventful train trip east, Louise is quickly recognized as extraordinarily talented by Ruth St. Denis (Miranda Otto) and her partner Ted Shawn (New York Ballet dancer Robert Fairchild), but her recklessness is a constant problem to Norma, especially after the girl takes up with a pleasant but overly accommodating soda-shop clerk (Andrew Burnap). Nor can Norma really keep a close eye on the girl, since as an orphan who was adopted out of a Catholic institution in New York, she’s obsessed with getting information about her birth parents—an effort that brings her into contact with the orphanage’s kindly, helpful immigrant janitor Joseph (Géza Röhrig). They will initiate a restrained romance, which hardly seems improper after revelations show that the Carlisle marriage is rather a sham, and why.

Under Michael Engler’s static, temperate direction “The Chaperone” coasts along at a stately pace defined by McGovern’s highly controlled performance as a somewhat prissy woman who finds her hidebound sense of conformity challenged by her attraction to Joseph, whom Röhrig plays with similar decorum. It’s basically the story of her gradual liberation from the stuffy conventions of the early twentieth century, and in that respect quite accommodating to modern feminist inclinations; but in telling it, Brooks’s part of the narrative is relegated to the back burner as a warning that giving in to those progressive tendencies without restraint can come at a painful personal cost.

What energy the picture has—apart from a scene in which McGovern reacts to a shocking secret in Alan’s life, and a couple sequences of New York nightlife—derives almost completely from the exuberance and sensuality Richardson brings to the young Louise. She captures the rebellious, rule-breaking spirit that characterized—and undermined—Brooks’s later film career with real conviction (her dancing skills are apparent, too); indeed, she’s so compelling that one wishes that Fellowe’s script had devised a way to show something of her life in cinema beyond a few posters on walls.

Instead, the story concludes by jumping ahead twenty years with a postscript set in Wichita where Brooks, her time in Hollywood over, has returned in defeat and depression. It was a visit Norma paid to her, we’re told, that sent her back east. Only the most meager information about her life in New York in later years is provided in a closing caption.

Like most Masterpiece productions, “The Chaperone” is nicely appointed.. Andrew Jackness’s production design and Candice Donnelly’s costumes capture the period carefully, and Nick Remy Matthews’ cinematography frames both interiors and exteriors cautiously to make the images convincing despite what was probably a fairly limited budget. Among the supporting players, Otto and Fairchild sketch incisive portraits as the dance school operators, and Blythe Danner has a touching single scene as a woman from Norma’s past.

As a portrait of an early twentieth-century Midwestern woman finding herself under the influence of progressive New York culture, “The Chaperone” is an example of historical fiction that will appeal to contemporary predispositions. The film is, however, stylistically pedestrian and narratively predictable, reflecting its roots in high-toned but staid TV programming. Nonetheless it’s inoffensive and pleasant, and perhaps it will prompt some farsighted filmmaker to think that a biographical treatment of Louise Brooks might be a fine idea, and that Richardson would be ideal in the lead. One can always hope.