© The TelegraphNicolas Sarkozy and Francois Hollande
Francois Hollande, the opposition Socialist candidate currently on course to beat Mr Sarkozy in April's election, allegedly called the president a "sale mec", which roughly translates as a "nasty piece of work".
He made the remark in a supposedly off-the-record briefing for reporters on Tuesday, but a truncated version of his jibe was revealed in the daily Le Parisien.
Although dismissed as being taken out of context by the Socialist camp, a cohort of outraged Sarkozy allies seized on the "insult".
Dominique Dord, treasurer of Sarkozy's UMP party, described the reported comment as "revolting" and said that Mr Hollande should pull out of the presidential race, little more than 100 days before the election.
"We are all deeply shocked," said the head of Sarkozy's UMP party, Jean-Francois Cope.
"This is not the standard expected of a presidential candidate," said government minister Nadine Morano, one of many other UMP party members to pounce on the reported comment. "I demand a public apology."
Le Parisien reported the term as an insult, but others present at the lunch said it was not a direct attack but part of an imagined dialogue in which Mr Hollande played Mr Sarkozy.
He said he was seeking to sell himself to the French with the message: "I'm the president of failure, a nasty piece of work, but in this difficult period I'm the only one capable of handling things. I alone have the bravery."
He continued: "He's going to present himself as Captain Courageous, courting unpopularity. He's a weak candidate because if that's how he's beginning his campaign it's unimpressive. France deserves better."
The Right went into blanket attack mode, with Valerie Rosso-Debord of Sarkozy's UMP party saying: "Frankly, it's a red card offence. You do not insult the president of the republic."
Interior Minister Claude Gueant branded Hollande's attack "unacceptable".
Reacting to the outcry, Mr Hollande said: "I've had enough of these rows organised daily (by the Right). I never use vulgarity.
"The French deserve better than the incessant use of comments that have been incidentally deformed. The French want a dignified campaign."
Mr Sarkozy is reportedly very cutting in private of Mr Hollande, once reportedly likening him to a sugar cube - hard on the outside but which melts when the political heat rises. The president is also no stranger to insulting outbursts.
In February 2008 he was caught on camera telling a member of the public who refused to shake his hand at the Paris agricultural show: "Get lost, you stupid bastard."
Recalling this episode, Bernard Cazeneuve, Mr Hollande's spokesman said: "Honestly, if Francois Hollande had said to Nicolas Sarkozy 'Get lost, you stupid bastard,' he would have had reason to complain. "But that's not the kind of thing Francois Hollande says and Francois Hollande will not be the president of 'Get lost, you stupid bastard'.
"This story is false. Francois Hollande is not in the habit of launching insults. He campaigns on the issues," he continued.
"And as to the way this non-event has been exploited by the UMP, I suppose that when Sarkozy calls Francois Hollande 'small' it's meant as a compliment, or that when he calls his supporters 'crackpots' he's just being friendly?"
Observers said that Mr Sarkozy's supporters were clearly hoping Mr Hollande would lose favour over the remark as his predecessor Lionel Jospin had in 2002 after he branded Gaullist rival Jacques Chirac as "old and worn out".
Mr Jospin was surprisingly knocked out of the presidential contest in round one.
Although seen as a formality, Mr Sarkozy is yet to launch his official re-election bid. Mr Hollande, meanwhile, is ratcheting up his campaign with meetings this week and a letter in Libération, the French-leaning daily, in which he blasted his rival as "the president of privileges".
Polls currently place Mr Hollande in first place, with Mr Sarkozy in second only just ahead of Marine Le Pen of the far-Right National Front.
I'm just so sure that Sarko is "outraged". More like he knows that he's going to lose, and will do anything to keep his cushy seat, so he's feigning outrage. Then again, I'm not sure Hollande will be much better...