The Icelandic actor-turned-director Benedikt Erlingsson achieved cult status with his tremendous 2013 film Of Horses and Men, in which horses were the facilitators and objects of passionate human love. Now he comes to the Critics Week sidebar of Cannes with this well-turned, well-tuned oddity, that brings Erlingsson’s career as a feature director to its Difficult Second Album moment. It is confidently and rather stylishly made, with the same eccentric poise that distinguished his equine success, and the same sweeping sense of landscape. There is a very good performance from Halldóra Geirharðsdóttir as Halla, a fortysomething choir conductor. Erlingsson shows a great flair for ideas, scenes, tableaux. But is it all encumbered with quirkiness? Is the quirk-imperative something that weighs it down?

What Woman at War has above all is a terrific premise; and by that token, a terrific opening scene. Halla is a secret guerrilla eco-activist who is campaigning against the energy corporations that are moving into Iceland. To protest, she sneaks out into the countryside and sabotages electricity pylons in remote areas – the hated pylons that are despoiling the landscape – using cordless circular saws to slice through the girders, and a bow-and-arrow to shoot disruptive cables over the power lines. (These scenes are not unlike those in Of Horses and Men where barbed-wire fences are cut in the course of a neighbours’ dispute.)

It is spectacular, dangerous work. No one would suspect the mousy Halla, and the cops keep detaining a suspicious-looking male tourist. Halla is obviously passionately committed to a campaign that might end in electrocution, death or imprisonment – or in the hated corporate raiders being driven away from Iceland and Halla becoming a national heroine.

But then one day she comes home to find a letter from the authorities: her application to adopt an orphan Ukrainian baby, made some years ago and all but forgotten, has been approved. Halla is to be a mum. And the weird truth dawns simultaneously on her and the audience. Has this eco-campaign merely been a displacement activity for her thwarted maternal instincts? Will she sheepishly admit to herself that she doesn’t much feel like bringing down electricity pylons now?

Another, more conventionally minded comedy might devote itself to the gradual fading of Halla’s radical enthusiasm as she gets nappies and toys ready for the new arrival from Ukraine. But Erlingsson is much quirkier and wackier than that; the police and security services become deadly serious about tracking the culprit down, giving the film the occasional look of a thriller, and things are complicated further with a twin sister for Halla (played by the same actor), a hippy-dippy woman called Ása who is preparing to go out to an Indian ashram, and whose twin status later furnishes a species of plot twist. There is also a lot of Icelandic folk music from a tuba, accordion and drums trio, and a rather beautiful singing group, whose performances turn out to be diegetic. That is, the camera pans around to show the musicians themselves, standing weirdly, incongruously in the background of the shot, variously trilling or parping away. It is a comic effect that is a bit distracting, subject to diminishing returns, and which ironises and undermines the action and obstructs your natural tendency to invest emotionally in Halla’s dilemma.

But it is an attractive and sympathetic performance from Geirharðsdóttir as Halla: a woman with a fierce and focused energy who has mysteriously concentrated all her efforts on an environmental campaign, but comes, perhaps, to see that there is no contradiction between pursuing that and wanting to be a mother.