‘I write about families,” Natalia Ginzburg said, “because that is where everything starts, where the germs grow.” The French-born writer and musician Alba Arikha clearly agrees, and has set her brilliant third novel firmly within the crucible of two families: the one her narrator is born into and the one she makes herself as an adult. The narrator is Clara, who, at the start, is a 16-year-old living in Paris and shares some biographical details with her author. (But not the fact her godfather was Samuel Beckett and she was named after his poem Alba.)

Life doesn’t sit still in your teens, and Clara’s is overturned when her father moves the family to New York for a teaching job. She rages against it (“I was overdoing it with my father. This was important to him. But I couldn’t help myself”), but what makes it worse is meeting the family who are moving out of the house they are moving into. Clara develops a crush on the son, Alexander, and the two hours she spends in his company will colour her life for decades.

Throughout her teenage years, from being dispatched to boarding school (“I decide to hate it”) to returning home, she has regular yearnings for Alexander. Arikha is excellent on the deep, narrow nature of a crush (“In my bedroom I hold many imaginary conversations with Alexander and, to my relief, I win the arguments every time”), where Alexander becomes a model nobody else can live up to because he is not bound by real experience.

Clara may not be happy in New York but her family are. “It’s easier to be a Jew here,” her father says, and she is “surprised because I hadn’t realised that being a Jew could still be difficult”. But she is tortured by “the extreme gap between what I know, what I love and where I am”. Alexander will return to Clara’s story, but meanwhile she marries another man. “My father is thrilled. He has always had a penchant for Englishmen.”

We must stop there for fear of spoiling the story, but in a sense that doesn’t matter anyway. Two Hours doesn’t do much new in terms of plot – young love lost, the trials of marriage and parenthood – but it does it all exceptionally well, with a rigour to the prose that recalls Rachel Cusk and an honesty – so clear it burns – that is reminiscent of Tove Ditlevsen’s great autobiographical trilogy.

Covering almost 40 years in 160 pages, it has scope and precision. The second half of the book is punctuated with set pieces – a parenting crisis, a potential affair – so intensely delivered that I had to set the book down to take a breath. Clara is not always sympathetic – she is blind to her own privilege and can be mean about others (she finds her husband’s alopecia patch “nauseating”) – but the sustained intimacy of her narrative binds the reader to her completely.

Two Hours is an impassioned account of the change we undergo as life pummels us – or, as Clara puts it, “the collision between my life story and the one I had imagined for myself”. To go back after the end, with everything she has been through, and see again her innocence and optimism at the start of the book, is heartbreaking. And if the end felt a bit too sudden to me, that’s mainly because I would have been happy to keep reading for ever.

• Two Hours by Alba Arikha is published by Eris (£15). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply