I trust Abderrahmane Sissako, director of this powerful plea for sanity, will forgive us if we start with a facetious reference. But, in the early scenes of Timbuktu, it is hard not to be reminded of a gag from one of Woody Allen's early funny films.

Islamic fundamentalists have taken over the Malian city of the title and are pressing home a series of rigid cultural restrictions. Football is banned and music forbidden. In one particularly absurd moment, the bullies insist that, as the rules now demand, an older man roll up the legs of his trousers.

One thinks of the dictator in Allen's Bananas who decreed that underpants now be worn on the outside. It is part of this film's singular power that it manages to slip from conscious absurdity to appalling atrocity with such confidence.

Timbuktu hangs around a Tuareg family – Kidane (Ibrahim Ahmed), Satima (Toulou Kiki) and their daughter (Layla Walet Mohamed) – who, living just outside the city, are drawn into the madness following an accidental tragedy.

Here we encounter a few tonal uncertainties. The family’s life is a little too idealised, playing guitar in their tent while musing mildly on life. The portrait is, indeed, not too far from the sort of image encountered in fantasised tourism commercials for more exotic destinations.

The softening is, however, to a purpose. Sissako, director of the highly regarded Waiting for Happiness, is not directing any sort of art film. Timbuktu is an accessible, propulsive drama that soaks up all kinds of vital ideas about our troubled world as it progresses.

Sissako does have some fun with preconceptions and idealisations. The family may be nomads living with ancient traditions, but they have a cow who – acknowledging an essential new technology for the wanderer – rejoices in the name “GPS”.

From the beginning, we are made aware of the fundamentalists’ hypocrisy. They claim to shun all western corruption, but remain addicted to their mobile phones and use the language of Madison Avenue when making their propaganda videos. The absurdity of their philosophy is elegantly expressed when a group of local boys play a complex game of football without a ball. (I’m sure such things used to happen in Northern Ireland on dreary Sundays during the dreary 1950s.)

In one engaging scene – that, again, perhaps, drifts into the arena of idealisation – a band of musicians, led by the charismatic Malian singer Fatoumata Diawara, host a late-night party that practically invites catastrophe upon their heads.

Timbuktu turns on its axis following the death of Kidane's ox and his clumsy attempts to exact retribution. Hitherto composed largely of static mid-shots, the film suddenly admits one very long, very beautiful long shot of our hero walking steadily across a gloomy, silt-laden river. We are clearly moving from satire to tragedy.

What we end up with is a film that adeptly meshes political anger with strong traditional narratives. Sofian El Fani’s cinematography is luminous. The music is uplifting. But the message ultimately is dire.

The trick with such works is to avoid didacticism and slip the lessons in with a compelling drama. Sissako profits from some very attractive, original performances as he manoeuvres us towards a series of striking visual set pieces.

Timbuktu will never eat up the multiplexes. But, in the past 12 months, it has gone to places that African films rarely go. It took the Ecumenical Jury prize at the Cannes Film Festival in 2014. It was nominated for best foreign language film at the Oscars.

That attention will, it must be hoped, help spread word about a film that says terrible things in a surprisingly engaging, often very funny voice. Not to be ignored.

Timbuktu is released May 29th 2015, and is is also avoiable to view on Volta.ie