The narrator of Deborah Levy’s witty scherzo of a “fiction” – “novel” isn’t the word for this uncategorisable book – thinks that Gertrude Stein would have liked Sigmund Freud. She imagines them enjoying a cigar together while their wives make small talk. Would Frau Freud “have exchanged her recipe for boiled beef with Alice B [Toklas]’s recipe for hashish fudge”? The two never met (though with her interest in the “bottom character” and his in the “unconscious”, Stein and Freud would have had plenty to talk about), but that barely matters. This book is full of things that don’t actually happen, of relationships that are not what the people involved suppose them to be, of digressions and fantasies and encounters that are imagined but never take place.

It all starts with a lost cat. The cat is called “it”: lower-case “i” followed by lower-case “t”. This causes all sorts of linguistic confusion, highlighting the way we use the word “it” to mean something indeterminate (as in the first sentence of this paragraph), or something trivial, or something tremendous. The phrase “lost it” recurs, the “it” meaning – variously – one’s mind, sympathy with Ernest Hemingway, daring to be as unconventional as Gertrude Stein, the stream of consciousness “flowing under the mowed and manicured golf courses on which men swung their clubs in the 21st century”, the temptation to smile while being undermined by a patronising man, the drudgery of housekeeping, the thing – which might be obedience or shame – that holds an artist back from becoming a modernist … or love, or one’s mother, or a black-and-white cat with one deformed ear.

The book doesn’t exactly have a plot, but there is a situation. Three female friends are in Paris. The narrator (English, single) is writing, or failing to write, an essay about Gertrude Stein. Eva (Spanish-Danish, married to a man in Seattle whom she sees once a week, if that, on FaceTime) is a graphic novelist. Fanny (French, polyamorous with three female lovers) is a financier.

Fanny is impatient, annoyingly often on her phone at mealtimes and capable of spite. Sexy and chic, she thinks Stein’s “knitted woollen stocking would have been erotically catastrophic” and says her “repetition drives me in-saane”. But she is also secretly vulnerable, wounded by her father’s homophobic rejection and more invested in the three-way friendship than either of the others. When the narrator is knocked off her bicycle, it is Fanny who comes to help, having first queued for eight minutes to buy a rum baba bouchon with a slice of roasted pineapple on top. It’s for the narrator – a kind thought – but Fanny explains to her that “if I was dead by the time she reached [me] she would eat it herself”.

Eva looks angelic, and the fuss about her lost cat makes her seem childish, but it gradually dawns on the narrator, and on us, that she is actually commercially astute and emotionally cool. Her all-white apartment is exquisite and so is the fat-free food she serves. She appoints herself the narrator’s assistant, says she will illustrate the Stein essay, and finally announces, without any consultation, that she will take over the project and write it herself. The reason her husband isn’t there is that he is building her a house. Whatever “it” is for her, Eva knows how to get it.

Suspended between these two new friends, the narrator, older and lonelier, moons around Père Lachaise cemetery and frets that however much she finds out about Stein’s life, she can’t get to the “it” of it. Late in the book a kind of romance starts up. Hunting for the lost cat, the three women come across an eligible man of the narrator’s age. He leads them for a moment into a Buñuelesque mystery. He also has a cat with a deformed ear. What’s going on here? He takes the narrator out to dinner, but this courtship is something else that fails to happen – all he wants from her is Eva’s phone number.

Despite the title, the action of the framing story takes place over one month, November 2024, the last month the three friends will be together in Paris, and the month of Donald Trump’s re-election. The narrator watches wars on her phone, the violence interrupted onscreen by adverts for vitamins or life insurance, and IRL by the bells of Notre-Dame.

Most of the time, though, her mind is in Stein’s lifetime, and she carries us there with her. Levy is not competing with Stein’s many biographers. She is writing a meditation, not a chronicle or an explanation. The narrator thinks that, for all her insistence on confining herself to simple words, Stein didn’t “believe in” being understood. “When I look at photographs,” she writes, “I cannot get into her eyes.”

Levy can, though, carry us into the Paris of Stein’s era and introduce us around. She chooses her quotes astutely. Seven lines from On the Road tell us all we need to know about Jack Kerouac’s vanity. A put-down from Virginia Woolf nicely punctures Walt Whitman’s self-righteousness. She has a great knack for summing up a character with one detail. Of the artist Chaïm Soutine: “a doctor had to remove a nest of bedbugs from his ear”. Of Marie Vassilieff, another artist: “When Modigliani arrived, drunk, looking for a fight, she lifted her arms and pushed him down the stairs. Then she carved the chicken.” Of Stein: “she was so forward‑looking that she never learned to reverse her Ford Model T”.

We are not to assume that the narrator is Levy – this is “a fiction”, after all – but of one thing we can be certain. Eva may announce that the essay on Stein will never get written, but here it is – odd, inventive and wonderfully entertaining – triumphantly proving her wrong.