Olivier Duhamel, who has described the allegations as “personal attacks”, is accused in the book, written by his stepdaughter Camille Kouchner, of abusing her twin brother when they were aged 14.
The book “La Familia grande”, which is due to be published on Thursday but has been serialised in L'Obs magazine and Le Monde, has shocked French intellectual circles given Duhamel's prominence and close connection to the elite.
While many commentators have seen France as being slow to break longstanding taboos over the abuse of minors this is not the first such controversy to make headlines over the last year.
Publisher Vanessa Springora, in a book published in January last year, accused prize-winning writer Gabriel Matzneff of abusing her while she was a minor. Film star Adele Haenel in November 2019 accused director Christophe Ruggia of sexually harassing her when she was in her early teens.
Haenel and other French actresses also in February last year walked out of France's Cesar awards after filmmaker Roman Polanski – who is wanted in the US for the statutory rape of a 13-year-old girl in 1977 – won best director.
Duhamel said on Twitter that following the allegations he was resigning from all his posts, including as head of the National Foundation of Political Sciences (FNSP) a body that oversees the hugely prestigious Sciences Po university.
“I am stepping down from my posts after being the target of personal attacks as I want to preserve the institutions in which I work,” said Duhamel, who also until now presented a show on Europe 1 radio and is an analyst on LCI TV.
Camille Kouchner, now 45 and a lecturer, and her twin bother are the children of France's former foreign minister and co-founder of the Medecins Sans Frontiers (MSF) medical charity Bernard Kouchner and academic Evelyne Pisier, who died in 2017.
Kouchner and Pisier separated and she went on to marry Duhamel.
“I was 14 years old and let it go ahead. I was 14, I knew and said nothing,” Camille Kouchner wrote in the book, according to the published extracts.
In the book, she names her brother only as “Victor” in order to protect his privacy. But Le Monde said he had read the text twice and was happy for his sister to speak on his behalf.
“I confirm that what my sister has written concerning the actions of Olivier Duhamel towards me is correct,” “Victor” told Le Monde.
In an interview with L'Obs, Kouchner said the book revealed to what extent Duhamel's and Pisier's group of leftist intellectual friends, some of them household names in France, knew what was going on.
“Of course, I thought my book might seem obscene because of my family's fame. Then I thought to myself, this is exactly what needs to be done,” she said.
In a statement released by his lawyer, Bernard Kouchner said that a “heavy secret that has been weighing on us for too long has happily been lifted. I applaud the courage of my daughter Camille”.