The French president, François Hollande, has said his country has “a problem with Islam” and that there are too many illegal migrants arriving in France.

He also suggested that today’s “veiled woman” could become a Marianne, the female symbol of the French republic, and attacked his rival Nicolas Sarkozy as “the little De Gaulle”.

The controversial remarks are published in a 660-page book, A President Should Not Say That: Secrets of Five Years in Office.

Hollande, 62, also spoke of the women in his life and how his actor girlfriend, Julie Gayet, wanted to be de facto first lady of France, which he said was a “hot topic” between them. He admitted he is feeling lonely and betrayed in the Elysée Palace, where he sometimes feels like a “ghost”.

The French leader, whose desperately low popularity ratings make it uncertain as to whether he will stand for a second term in office, made the comments during more than 60 interviews with Le Monde journalists Gérard Davet and Fabrice Lhomme.

The subjects covered range from Hollande’s dismay over the national football team and the new generation of players (“they’ve gone from badly educated kids to ultra-rich stars with no preparation”) to his 2012 presidential rival Sarkozy, whom he described as “a Duracell bunny who is perpetually agitated” and full of “vulgarity and cynicism”.

But Hollande confided that he would not hesitate to vote for Sarkozy if it was a choice between his predecessor and Marine Le Pen, the leadeer of the far-right Front National.

It was his comments on Islam that could prove the most controversial.

The book quotes Hollande saying: “It’s true there is a problem with Islam … and nobody doubts that. There’s a problem with Islam because Islam demands places (of worship), recognition. It’s not that Islam is a problem because it’s a religion that is in itself dangerous but because it wants to assert itself as a religion on the Republic. What might also be a problem is if Muslims don’t criticise acts of radicalisation, if imams behave in an anti-republican way.”

He added: “The veiled woman of today will be the Marianne of tomorrow … because, in a certain way, if we offer her the right conditions to blossom she will liberate herself from her veil and become a French woman, while remaining a believer if she wishes, capable of carrying with her an ideal ... Ultimately, what are we betting on? That she will prefer freedom to subservience. Perhaps the veil is a kind of protection for her, but that tomorrow she will not need it in order to be reassured of her presence in society.”

Critics said the French president was – perhaps inadvertently – suggesting women in France who chose to wear veils were not French and preferred to be subservient.

On immigration, Hollande told the authors: “I think there are too many arrivals, immigrants who shouldn’t be there … we teach them to speak French and then another group arrives and we have to start all over again. It never stops … so, at some point it has to stop.”

Laurent Wauquiez, president of the opposition centre-right Les Républicains, accused Hollande of being “willing to barter the symbol of the French republic for political Islam”. He said Hollande was “selling off the most powerful symbols of the French republic on the cheap”.

On French footballers, Hollande allegedly called some of them “guys from housing estates without bearings, without any values, who left France too early … they need weight training on their brains”.

He said he did not want to officialise his relationship with Gayet, 44, who he described as “a fine girl” and admitted she was “suffering from this situation”.

The president’s relationship with Gayet led to the break up with Valérie Trierweiler, a Paris Match journalist, for whom he left Socialist government minister Ségolène Royal, mother of his four children. Hollande said Trierweiler had an “obsession” with Royal, but he admitted: “The woman I am closest to is Ségolène … she is there when I need her.

“What weighs heavily on me is not having a family life. I liked family life a lot … at the Elysée you cannot have a private life. There is no time to be happy.”