Denis Villeneuve’s sci-fi contact drama is dreamy, freaky, audacious. It skirts the edge of absurdity, as anything like this must, but manages to keep clear, and it includes a big flourish in the manner of early films by M Night Shyamalan, which adroitly finesses the narrative issue of what exactly to do with a movie about aliens showing up on Earth.

I have been agnostic about this kind of movie recently, after the overwrought disappointments of Christopher Nolan’s Interstellar and Jeff Nichols’s Midnight Special. But Villeneuve’s Arrival is both heartfelt and very entertaining.

As is now expected with this kind of film, the protagonist is a flustered, bewildered civilian with special expertise, brusquely pressed into service by the military, which has got the spacecraft surrounded in the short term.

Amy Adams is Dr Louise Banks, a professor of comparative linguistics with nothing and no one in her life but her work. But as it happens, Dr Banks was once seconded as a military adviser to translate a video of insurgents speaking Farsi. So when a dozen giant spaceships land in 12 different locations on Earth (including Devon – sadly there no scenes there), each looking like a bisected rugby ball standing on end, a bunch of army guys led by Col Weber (Forest Whitaker) show up on Louise’s doorstep, demanding she come with them to help translate what the aliens are saying. Why, you ask, did they not approach Noam Chomsky, with his understanding of “deep structure” in language? Perhaps Prof Chomsky did not care to help America’s military-intelligence complex.

At any rate, Louise’s liaison is the flirtatious Ian Donnelly (Jeremy Renner), a military scientist who, in a stereotypical and fallacious way, equates his masculinity with science and affects to despise what he sees as the softer discipline of linguistics. Michael Stuhlbarg plays Halpern, the glowering CIA chief. But unbeknown to them, there is a secret tragedy in Louise’s life: a lost child, dead of cancer in her late teens. Her attempts to communicate with the aliens cause painful but illuminating echoes in her mind.

If a lion could speak, said Wittgenstein, we would not understand him. Does the same go for aliens? Spielberg solved this issue elegantly in Close Encounters of the Third Kind by making the form of communication a five-note musical phrase, ending questioningly on the dominant. Villeneuve’s solution is more literal. The aliens have a code which – a little preposterously – Louise finds herself more or less able to crack, with the crowdsourced expertise of the other 11 human-contact teams around the globe. But it is her human intuition, vulnerability and spontaneity that finally enable her to reach out to the visitors.

Inevitably, these “contact” moments are where the film’s real impact and atmosphere have to be. And Villeneuve doesn’t disappoint in sequences of eerie and claustrophobic strangeness – though I concede the film is most effective before the physical form of the aliens is revealed. There are also touches of comedy: Ian and Louise decide, for convenience’s sake, to nickname two aliens Abbott and Costello – maybe in homage to the linguistic misunderstanding in the duo’s famous routine about a baseball team’s positions.

By coolly switching focus to political intrigue and betrayal within the human ranks, Villeneuve keeps a grip on his story and creates ballast for its departure into the realms of the visionary and supernatural. And he also prepares us for the film’s sense that language itself, freed of our usual sense of its linear form, might be more important than anyone thought. (I wonder if Villeneuve has seen the 2010 documentary Into Eternity, by Danish film-maker Michael Madsen, about attempts to devise a new universal language to label underground repositories of nuclear waste – labels whose warnings have to be understood by future humans whose language has evolved away from what we know now.)

Arrival is a big, risky, showy movie which jumps up on its high-concept highwire and disdains a net. And yes, there are moments of silliness when it wobbles a little, but it provides you with spectacle and fervent romance.