The history of the music business is full of charismatic, handsome frontmen.

But weird ones - that's another thing. The list of memorable "outsider musicians" is short, and no top five would be complete without Captain Beefheart, Daniel Johnston and Britain's own truly bizarre Frank Sidebottom.

The alter ego of the late Chris Sievey, Sidebottom was a comedian and pop star distinguished by his large papier-mâché head, which he never took off, a cartoon visage of huge round eyes, slicked black hair and pouting mouth. Creepy, for sure, but Sievey's anarchic Northern wit made for a likeable and very funny creation.

Frank, the movie, is as much a curio as the man who inspired it, and just as engaging. While it's co-written by Jon Ronson, the journalist and documentary-maker who was once in Sidebottom's band, and features a musical Frank with the recognisable head, it's not about Sidebottom/Sievey per se, but a fictional variation. Free of biographical necessity, the result is a tale of misfits in pursuit of pop stardom that is universal.

The central character is actually a more familiar wannabe - Jon (Domhnall Gleeson), a young man still living with his parents, spending his spare time penning awful lyrics and day-dreaming of a musical career. It doesn't seems likely, until a chance encounter with the impossible to pronounce band Soronprfbs changes his life.

The band urgently need a replacement keyboard player for that evening's performance. Jon points out that he doesn't know any of their songs. "Can you play C, F and G?" asks manager Don (Scoot McNairy). That'll do.

The gig is disastrous, but leads to Jon's full membership of the band, which comprises singer/songwriter Frank (Michael Fassbender), who is never seen without his fake head and lives in his own little world, the Theremin-playing and foul-tempered Clare (Maggie Gyllenhaal), who is hostile towards the new member, French guitarist Baraque and silent drummer Nana. Together they might best be described as early New York punk, their DIY wall of sound whirling around Frank's alien persona.

During months spent recording an album in an isolated Irish shack, the inexperienced but eager Jon slowly wins the others over. It doesn't hurt that he gives them his savings, or that Frank comes out of his shell (if not his head), revealing a sweet-tempered, optimistic, musically ambitious band leader, sincerely excited by the naïve newcomer's pop sensibility. "I always wanted a band," he exclaims, "who shared my dream of making really likeable music."

But we never forget that a man who even wears his fake head in the shower has issues. And as funny as much of the film is, there's no shortage of clues to mental illness and collective dysfunction - which boils over when the band is invited to a music festival in the US.

Material such as this could have gone in so many directions, from the inane to the breezily eccentric to disturbingly dark. Here, director Lenny Abrahamson (Garage, What Richard Did Next) skilfully walks the knife edge of tragi-comedy. It's a surprisingly profound film, at the heart of which is another great performance by Fassbender, who never ceases to amaze.

Like Daniel Day Lewis, Fassbender is an actor who diverts us from leading-man looks (in this case, obscuring them completely) with intense character performances. He follows the vile plantation owner of 12 Years A Slave with the antithesis, a character who is at once damaged, inspirational and enigmatic, all conveyed through this outlandish disguise. Incidentally, Frank is no mean performer, and Fassbender's singing suggests an alternative career should he ever want one.