To European art house sensibilities there is no stranger landscape than the American psyche, and no premise too improbable to indulge in a surreal vehicular excursion. Also: nearly every American encountered seems colourfully crazy, dangerous, grotesque, narrow-minded, fantastically generous and/or a rich braggart - preferably with a deep-fried Southern accent. Throw in some iconic natural wonder - the Grand Canyon, Monument Valley or, in this case, the Great Salt Lake of Utah - plus a cameo from Harry Dean Stanton, and voilà, you have your scenic, philosophical road trip. The self-discovery honours here fall to Sean Penn's traveller in a characterisation that is transformative writ large.

Director and screenwriter Paolo Sorrentino has won scads of awards for The Consequences Of Love, The Family Friend and Il Divo. But we're not entirely sure what he's trying to pull off in his first English-language project, written with Umberto Contarello. It's a patchwork quilt of encounters in many colours and moods. There are vignettes of warmth, notably with women: in Cheyenne's home life with his practical, kind and good-humoured wife of 35 years, Frances McDormand's Jane, who we would have liked to have seen more of; in his friendship with teenaged number-one fan, Mary (Bono's daughter Eve Hewson); and with the lonely single mum, Kerry Condon's Rachel, who takes him in when he straggles into New Mexico. There is humour, from good lines ("Rock stars shouldn't have kids because you run the risk of your daughter becoming a wacky stylist") and from the sheer incongruity of Cheyenne, who sticks out like a sore thumb in small-town, strip-mall America, as a man on a mission. There is cool: David Byrne playing himself as friend and sage to the lost protagonist. There are also puzzling subplots, narrative non sequiturs, overt symbolism and The Holocaust, its consequences touching characters who know nothing about it.

Penn's bored, deadpan, sorrowful Goth relic, with his high, flutey little voice and heavy, smeared make-up, is a gob-smacker - funny, insecure, but with a childlike honesty and courage, and near miraculously touching. This also scores for originality, unpredictability and cinematography (Luca Bigazzi); less so for dubious taste and bewildering twists.