PARIS (REUTERS) - Conservative Alain Juppe tightened his grip this week on France's presidential race, cementing his place as favourite to represent the centre-right, while Socialist President Francois Hollande was wounded by the publication of a damaging new book.

Mr Hollande's as yet unofficial re-election campaign has been thrown off course by the book, "A President Shouldn't Say That," written by two respected journalists from Le Monde newspaper who met him 61 times.

The deeply unpopular leader is quoted as calling members of the judiciary "cowards" and saying France has "a problem with Islam", in comments that led even some of his allies to question on Friday (Oct 14) whether he should stand again.

Mr Hollande apologised in a letter to outraged judges, but even some close supporters say the damage is done.

"I still think he wants to stand, but he has not made the task any easier," Mr Jean-Christophe Cambadelis, Socialist Party Secretary and one of Mr Hollande's closest allies, told RTL Radio, advising him to speak out soon about the book.

Prominent lawyer Jean-Pierre Mignard, also close to Mr Hollande, told Europe 1 radio the comments about magistrates - in the context of a row between Mr Hollande's former justice minister and some members of the profession - were"inappropriate".

Mr Claude Bartolone, president of the National Assembly and a Socialist party heavyweight, also weighed in. "I'm asking myself questions about his desire (to stand)," Mr Bartolone said in a column for La Provence regional newspaper. "A hesitation is emerging. I have told him I am stupefied (by the book). There is a pressing need to explain whether he really wants to be a candidate."

Mr Juppe came top in an Oct 3 poll which asked voters who would make a good president, with a score of 47 per cent. For months now, polls have shown him as the most likely candidate to move into the Elysee presidential palace next May.

In the same poll, Mr Hollande scored just 16 per cent, in 12th place behind even some of his rivals on the left.

The president has been even more unpopular in past polls, in large part because of his record on the economy, where growth is sluggish and unemployment stuck stubbornly around 10 per cent.

Voters are also questioning his government's competence on security and immigration, given that over 230 people have been killed in Islamist militant attacks since early 2015.

Mr Juppe's "happy identity" campaign is shaping the political debate about France's capacity to deal with a large influx of Muslim migrants and overcome religion-based tensions following the attacks in Paris, Nice and elsewhere.

The vision stands in contrast to the more divisive rhetoric of his main centre-right rival, former president Nicolas Sarkozy, but amounts to a declaration of faith rather than a policy proposal. It is that France can reconcile its Christian roots and secular tradition without marginalising its Muslim and Jewish communities, the largest in Europe.

Mr Juppe, 71, a former prime minister, sought in a blog last June to explain his slogan. "I will not endorse this cautious, anxious, almost neurotic idea of unhappy identity (for France)," he said. "For me, identity means unity in diversity."

Just ahead of Thursday (Oct 13) night's debate in which seven candidates set out their policies for the centre-right primaries on November 20, Opinionway pollsters put Mr Juppe on 42 per cent of the first-round vote, versus 28 per cent for Mr Sarkozy.

After the debate, watched by some 6 million people, an online survey of 885 voters by polling firm Elabe for news network BFM TV said he was the most convincing for 32 per cent of would-be primaries voters, compared with 27 per cent who favoured the ex-president.

Assuming Mr Juppe does win the nomination, polls have repeatedly shown him reaching the second-round run-off of the presidential election itself, and defeating Ms Marine Le Pen, leader of the far-right National Front.

His relative popularity is so high versus the abrasive Mr Sarkozy and the troubled Mr Hollande that some Socialist voters are considering voting in the centre-right primaries to make sure he wins the ticket so that they avoid a Sarkozy-Le Pen choice.

Mr Hollande has said he will decide in December whether to stand. The Socialist party primaries are set to take place in January.