Small town, long grass, children running. In an Australian film, we might expect to hear sweeping orchestral music over these opening images, or, having been informed that the year is 1958, a rock’n’roll standard by Johnny O’Keefe. But the choice for The Sapphires is arrestingly odd: ‘Run Through the Jungle’ by Creedence Clearwater Revival, vintage 1970. It’s not Australian and it’s out of time, but it works, instantly kicking things into gear.

The song sets up a storyline. Three Aboriginal sisters, Gail (Deborah Mailman), Julie (Jessica Mauboy) and Cynthia (Miranda Tapsell), plus their cousin Kay (Shari Sebbens), like to sing American country and western songs. When Dave (Chris O’Dowd), an Irish visitor with vague connections to the music industry, appoints himself their manager, he makes one stipulation: the sound has to be black soul. Since by this point we are in 1968, The Sapphires head off to Vietnam to perform.

Films about the trials and tribulations of show business tend also to be about themselves – their place in entertainment history, and their prospects for box office success. So The Sapphires, a film about indigenous Australian traditions mixing it with the wider world, is a bold gesture, aimed at impressing the international marketplace. It tries to accommodate as many cultural tastes as possible – and succeeded in attracting America’s Weinstein brothers as executive producers.

Director Wayne Blair juggles this busy material well. It’s the kind of movie that renders standard critical demurrals – that some of the comedic mugging is overdone, that plot links don’t always make sense, that situations at times tip over into unreality – entirely beside the point. Rather, it is the mark of a good mainstream film that it can fly over mundane plausibility issues and niggling narrative questions, with a heightened air of wish-fulfilment fantasy.

Much of the charm of The Sapphires for Australian audiences comes from the way it deliberately falls short of the slick Hollywood music biopic model. It is like a canny mix of Dreamgirls (2006) and Alan Parker’s gritty The Commitments (1991) – with the superb Mailman on hand to deflate any looming sentimentality with her insults and hard truths. Amid all the feel-good vibes, the film even manages, with a salutary shock, to touch upon issues such as the Stolen Generations; it handles this mix of entertainment and populist politics better than Baz Luhrmann’s Australia.

The Sapphires lacks one thing: a big extended musical performance scene. That’s symptomatic: at the end, the film returns to its real-life origin in the indigenous community and, in this sense, turns its back on globalised showbiz. At least it does so on its own proud terms.