First-time Chilean director Francisca Alegría turns up the arthouse dial past eleven right from the name of her debut feature. The Cow Who Sang a Song into the Future is a conspicuously poetic title that gives every impression that we’re in for a hardcore cine-patience tester. I have to admit that it made my heart sink. But while, yes, TCWSSF is a dreamy magical realist fable with an environmental message, Alegría weaves into her tale an emotionally satisfying, gripping family drama, with singing cows – and fish too.

It begins with the fish, dying by the shoal-load on the banks of a river, poisoned by pollution from a nearby factory. As the fish die, a woman gasps to the surface of the water. This is Magdalena (Mía Maestro), who drowned herself decades ago. Now she is back from the dead as if time stopped – still gorgeous, still dressed in the boilersuit she wore when she drove her motorbike deliberately into the river. Magdalena’s husband collapses when he spots her outside a mobile phone shop. Their adult daughter Cecilia (Leonor Varela) – just a girl when her mum died – drives from the city with her two kids to look after him at the family’s dairy farm.

The film is a mediation on damage and repair. The point, I think, is that our resilience, like the natural world around us, is fragile and interdependent. In the river, when the fish die, the swans starve. Childhood trauma makes Cecilia cold, unable to connect with her own kids – the eldest especially, a transgender girl (beautifully played by newcomer Enzo Ferrada Rosati). It’s a thoughtful film, tender, hopeful, with some knockout bovine performances too. Though in the end the cows don’t do any actual singing; they leave the dirty work to human stand-ins.

• The Cow Who Sang a Song into the Future is released on 24 March in UK and Irish cinemas.