Justin Kurzel's blistering, blood-sticky new screen version of Macbeth unseams the famous Shakespearean tragedy open from the nave to the chops, letting its insides spill out across the rock underfoot. Kurzel's chilling debut feature, the 2011 true-crime thriller Snowtown, suggested the then-37-year-old Australian filmmaker was a talent to watch. But this towering, consistently ingenious film establishes him as a director to cherish.

Built around a pair of cosmically powerful performances from Michael Fassbender as Macbeth and Marion Cotillard as Lady Macbeth, Kurzel's film, which has had its world premiere at the Cannes Film Festival, retains the play's Scottish Middle Ages setting and some of Shakespeare's words.

But the pared-down adaptation by Jacob Koskoff, Michael Leslie and Todd Louiso feels jagged and spare – the bleached, modernist carcass of the original verse – while the sheer innovation of the staging lends a flesh-creeping freshness to every familiar toss and turn of Shakespeare's plot. Tonally, it is far closer to the fractured poetry of T.S. Eliot's The Waste Land than Game of Thrones, yet the battle sequences have a serious, blockbuster beauty and heft, with thunderous, slow-motion combat backlit by blood-red sun rays, mist and smoke.

This is in evidence right from the opening shot, which is not of the expected three witches, but the blue-white body of a boy, laid to rest on a carpet of heather and moss. A small funeral party surrounds him, at the head of which are Macbeth and his wife, mourning this tiny, would-be heir to the thanedom of Glamis.

The loss of this child broods over the ensuing carnage like the clouds of mist that constantly roll across the Scottish landscape, which gapes jaggedly below, like a dragon's jaws. Both Macbeth and Lady Macbeth are fascinated by power, but they're also terrorised by thoughts of the void beyond it, and every increasingly bloodthirsty decision they make is steered by their existential desperation to endure.

After seeing Fassbender and Cotillard in these roles, the thought of ever seeing anyone else play them fades into irrelevance. Fassbender makes Macbeth a totally plausible despot, bringing him roaring out of the shadows of his often-more dominant wife. Yet Fassbender makes his character's hunger for power feel entirely human, and perhaps even a little perversely noble, though his sanity ebbs away.

"O! Full of scorpions is my mind" is a line Fassbender was born to say, and he delivers it perfectly, with an anguished smile that suggests he can feel the creatures pattering up his brain stem.

And then there's Cotillard, who has the cold, ivory composure of a Lewis chess piece, complemented by some Black Swan-like make-up and tremendously scary, shroud-like costumes. But again, through all the scheming and blood-letting, the actress never loosens her grip on the character's humanity.

When Lady Macduff (Elizabeth Debicki) and her children are murdered in revenge for Macduff's treachery, Kurzel has them burnt at the stake with Lady Macbeth in attendance, and Cotillard plays the moment perfectly, shedding a horrified tear at the depths to which she and her husband have sunk.

It's this self-interested act of mass murder – the snuffing out of the entire Macduff line for the sake of her own, stunted family's temporary advancement – that sends her tumbling onto the rocks of madness. And if that strikes you as a smart and laterally thought-out adaptational flourish, just wait until you see the metaphysics of the ghostly dagger scene, or Lady Macbeth's climactic, soul-tearing soliloquy, or exactly how Macduff himself (Sean Harris, spectral and supremely unnerving) brings Birnam Wood to Dunsinane.

David Thewlis, Paddy Considine and Jack Reynor, as Duncan, Banquo and Malcolm respectively, vanish into their roles, without a hint of the rep-company starchiness that second-tier Shakespeare characters can engender in actors determined to "do justice to the Bard". Justice is done here through a constant hacking away and boiling down, borne of a determination to get right to the heart of the original play. The "Double, double" incantation is gone from the potion-mixing scene, as is the porter's comic interlude, as is the character of Donalbane, who's been (entirely rightly) judged superfluous to this telling.

Though it almost certainly wasn't planned this way, Kurzel's Macbeth feels like the first post-referendum British film: its themes of destiny and hubris are scorchingly relevant. The tragedy of Macbeth feels as vital and visceral here as it did in the hands of Roman Polanski and Akira Kurosawa, whose previous retellings are as good as Shakespeare on film gets. Kurzel's version stands respectably beside them, and there can be few higher compliments than that.