Starring Domhnall Gleeson and Michael Fassbender. Rated 14A.

It doesn’t take any awareness of the late U.K. comic Chris Sievey and his main creation, Frank Sidebottom, to enjoy Frank. But the peculiarities of that TV and standup alter ego—which found the comic singing and telling stories from inside a huge papier-mâché head adorned with eerily blank features—could not be forgotten by the cast and crew behind this stingingly original rock-band comedy, which gets more passing strange as it moves along.

Initially, the film follows the travails of the gormless, ginger-tressed Jon, played by Domhnall Gleeson, late of About Time and son of Brendan Gleeson (who stars in this week’s stark Calvary). It’s a deceptively thorny coming-of-age gambit that serves to introduce everyone to a particularly unmerry band of pranksters, led by the titular Frank, played in another change-of-pace role by the Irish-German Michael Fassbender—this time inside a globular mask very similar to the one described above.

Fascinated by the musings, gyrations, and mad exhortations of this oddly charismatic figure, Jon, a nascent keyboard player who still lives with his parents, has a chance encounter with the American band, and is invited to decamp with them to rural Ireland. He yearns to understand what drives the creative spirit—to “find out what’s going on inside the head inside that head”. To do so, he must penetrate barriers put in place by band manager Don (Scoot McNairy), a bass player and drummer who say almost nothing in English (François Civil and Carla Azar), and, most obsidian of all, the mysterious Clara (Maggie Gyllenhaal), who—when not playing her menacing theremin—violently pushes neophyte Jon away from volatile genius Frank.

The multilayered effort is skillfully directed by Ireland’s Leonard Abrahamson, from a sharply defined script by Jon Ronson (The Men Who Stare at Goats) and Peter Straughan (Tinker Tailor Soldier Spy). It’s almost classically divided into movements, each with a different setting and tone. In the final, slightly shakier section, built around the social-media buzz Jon has been rather maniacally building, Frank takes Austin’s South by Southwest by storm—but not with the climate change everyone’s expecting. If you think you have a head for making art, or getting famous, the unforgettable Frank was made for you.