In 1971, Deirdre Bair achieved one of the great literary scoops of our times. Armed with a recently completed PhD and an abandoned career as a journalist for Newsweek, she persuaded Samuel Beckett to let her write his biography, a prize commission that had been denied to many male Beckett scholars twice her age. Maddeningly for those scholars, Bair had used the most straightforward of means: she simply wrote to the famously guarded Beckett, out of the blue from her home in Connecticut, and set out her proposal. He wrote back by return and asked her to come to Paris to see him.

That meeting is the starting point for this insightful and gossipy memoir of a biographer’s voyage around two towering subjects – after spending seven years on Beckett, Bair spent a further decade circling his near neighbour Simone de Beauvoir. Beckett greeted Bair in the lobby of the Hotel du Danube on Rue Jacob, with amused curiosity: “So you are the one that is going to reveal me for the charlatan I am,” he said. He initially agreed to “neither help nor hinder” Bair in her efforts, but over the years that followed, he sat down with her many times, helped her to navigate his written archive and introduced her to his legion of friends and acolytes.

What followed was a classic case of that strange dance between subject and biographer for possession of a life. Beckett insisted on certain caveats. When Bair, then 36, pulled out a notebook in their second meeting, Beckett jumped up from the cafe table, outraged – the author of Krapp’s Last Tape could not countenance any lasting evidence of his spoken words. “No pencils. No paper. We are just having conversations. Just two friends talking. Don’t even think of a tape recorder.”

Bair countered this obstacle by learning the questions she wanted to ask by heart from cue cards before each meeting with Beckett. Immediately after their talk was done, she ran back to her hotel room, and using the cards as aides-memoires, wrote down all she could remember of what had been said. So intimate was the result when it was published in 1978 that the academic Beckett industry – the Becketteers as Bair calls them – sought to undermine Bair’s methods. A question that appeared to be on the lips of many rival scholars was finally voiced to her in an interview by a local news reporter: “How many times did you have to sleep with Beckett to get this scoop?”

The answer was none. On many of her summer visits to Paris, Bair had her husband and two children with her; though Beckett was never less than gentlemanly with her, several of his former publishers, editors and friends assumed a quid pro quo for engaging with her literary endeavour. Frenchmen, she suggests, were usually quite direct in those assumptions; conversations would be prefaced with the line: “Are we going to bed?” When Bair told them no, that was the end of it. Others, such as Beckett’s favourite actor, Patrick Magee, were reluctant to cooperate unless they were to be invited to stay over.

In all of this intrigue, Bair retained a reporter’s savvy, as well as an academic’s rigour in getting near the truth. As a younger woman, all she had ever wanted was to be a journalist. By her mid-20s, trying to cope with deadlines and two small children, she determined her second vocation. She originally thought of calling this book The Accidental Biographer.

The final title suits it better. Using her detailed diaries and notes of the time, Bair conjures the atmosphere of the city in which her two subjects lived – never forgetting her own excitement and trepidation, and frustration at moving between salon and cafe-tabac in a sometimes comical search for their stories. Though Beckett and De Beauvoir lived almost on the same street, they loathed each other – an animus rooted in De Beauvoir having rejected one of Beckett’s early stories for the literary magazine she edited with Jean Paul Sartre, Les Temps Modernes. Invariably, when meeting the French woman, Bair would be dodging the Irish man.

Bair’s courtship of De Beauvoir and her circle was no less complex than her battles with the Becketteers. Bair was first brusquely invited to visit the author of The Second Sex on a date that she realised was her subject’s 73rd birthday. She is terrific at recalling the awkwardness and anxiety of that prospect. After much deliberation as to etiquette, Bair arrived at the door of De Beauvoir’s apartment at 6pm clutching a half-dying bunch of flowers, expecting a party. De Beauvoir opened the door in a ratty bathrobe wanting immediately to get to work.

Bair’s account of their sessions together are a case study in rival strategies of reticence and disclosure. When the interviews went well, the pair concluded with a Scotch that had been judiciously watered down by De Beauvoir’s companion and adopted daughter, Sylvie. On other occasions, Bair’s questioning was met with sudden rage; once, she was pushed by De Beauvoir out of the front door.

Bair, like all biographers, kept going back right up to the end of De Beauvoir’s life – there is a remarkable set-piece description here of the writer’s funeral cortege through the streets of Paris. Inevitably – and typically candidly – the biographer’s personal grief quickly gives way to a different, writer’s emotion as she realises that her final chapter is redundant: “Now I have to write this bloody book all over again.”

• Parisian Lives: Samuel Beckett, Simone de Beauvoir and Me by Deirdre Bair is published by Atlantic (£18.99). To order a copy go to guardianbookshop.com. Free UK p&p over £15