Maylis Besserie does not lack for daring. Her novel is a fictional account of the last months of Samuel Beckett’s life, which he spent in a Paris nursing home, Résidence Tiers Temps. As she says in an author’s note, the book “reconstructs a version of Beckett from real and imaginary facts, as if he were a character at the end of his life, like those who inhabit his own work”.

To set out to portray a master stylist, the author of Molloy, Malone Dies and The Unnamable, would daunt the most experienced writer. That this is Besserie’s debut, the first part of a projected “Irish trilogy”, is remarkable; that she carries it off so convincingly, with such elan and poetic force, is a wonder.

Fittingly, the narrative is in the first person – or the last person, as Beckett would say – as the old and ailing writer clings to the unravelling shreds of consciousness. The chapters in Beckett’s voice are interspersed with fictional medical reports on his condition by the home’s nurses, doctors and psychiatrists. These toneless pages set up a telling counterpoint against the rich musicality of the main body of the book. Besserie does not mimic the style of Beckett’s threnodies, yet she evokes, subtly and with great skill, a fitting intensity, bleak lyricism and black humour.

Readers who know Beckett’s work will note the echoes that resound here of the postwar trilogy, in particular, but also of many of the plays, and of later, astringent texts such as Ill Seen Ill Said, The Lost Ones and Stirrings Still. There are passages that conjure up with eerie immediacy the voice of Beckett’s derelict narrators – for it is all one voice, really – by turns declamatory, piteous, bitter and scurrilously funny.

Asked to say why he chose the title Company for one of the late texts, Beckett replied that, well, a book is company. Besserie’s version of the writer spends much of his time wandering among familiar shades in the land of the dead. Most precious of his lost ones is his wife, who died on 17 July 1989, just before the narrative opens. “She is dead. I have to remind myself constantly – Suzanne is not in the bedroom. She is not with me. She is no longer present.” Contrast, or compare, with the opening of the first novel in Beckett’s trilogy, Molloy: “I am in my mother’s room. It’s I who live there now.”

Beckett’s mother, the formidable May, is the other of the two poles between which the novel swings and sways. And talk of his mother inevitably leads to thoughts on the mother tongue. He recalls his time working for James Joyce when he was writing Finnegans Wake. “I type his English that is full of Ireland. He spits out page after page, the Ireland of our mothers … I took a long time to be cured of it.”

He wonders why he didn’t kill his mother. It would have been, he says, “a happy escape” – for both of them, we surmise. Yet in Besserie’s novel there are exquisite and moving passages through which May paces like her namesake in that late dramatic masterpiece Footfalls: “Like the wind that blows the dead branches, ready to fall, the light ones that rest on the living in the hope of holding them back, my mother’s trembling hands were placed on the pane of glass in the hope that the pane might keep them in place. To no avail.”

Another of his lingering ghosts is that of Lucia, Joyce’s doomed daughter. She was in love with Beckett and was spurned by him, and spent most of her long life in psychiatric clinics. Beckett never ceased to feel guilty about his treatment of Lucia. “The words left her. Everyone left her.” Here, as elsewhere, Besserie presents us with Beckett the poet of finality, of straitened ways and dire straits, the Beckett who was, as she has him say, “inapt for the world”.

Yell, Sam, If You Still Can is the work of a writer already in command of a resonant style and a broad artistic reach. There is no doubt she will do notable work in the future, considering that this is her first book – which was awarded the Prix Goncourt du premier roman in her native France. Praise is due also to Clíona Ní Ríordáin. Though the title is a mistake – why not The Third Age, as in the original French? – little seems to have been lost in translation. Indeed, the book reads as if it had been written in English, with much wordplay carried over deftly and inventively from the French. And there are good jokes. Here is Beckett struggling to do the bidding of his physiotherapist and rise from the floor without using his hands: “Tried again. Failed again. No better.”

• Yell, Sam, If You Still Can by Maylis Besserie, translated by Clíona Ní Ríordáin, is published by Lilliput (£13). To support the Guardian and the Observer buy a copy at guardianbookshop.com. Delivery charges may apply.