Socialist flag-bearer François Hollande, who will face Sarkozy in April's election, allegedly called the president a "sale mec" – literally a "dirty guy" and roughly equivalent in force to a term like "nasty piece of work".
Tuesday's lunch was supposedly an off-the-record briefing for reporters, including one from AFP, but Hollande's taunt was partially revealed in the daily Le Parisien, drawing outrage from the right.
Le Parisien reported the term as an insult, but other journalists at the lunch interpreted the phrase as part of an imagined dialogue in which Sarkozy described himself in unflattering terms in order to appear tough.
Imagining himself in the mind of Sarkozy, Hollande said: "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'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," he continued.
Several of Sarkozy's ministers and supporters in parliament denounced the insult. Valérie Rosso-Debord of Sarkozy's UMP party said: "Frankly, it's a red card offence. You do not insult the president of the republic."
Interior Minister Claude Guéant branded Hollande's attack "unacceptable" and several other ministers demanded a public apology from the opposition leader.
Sarkozy is reportedly privately very caustic about Hollande, and his career has also been marked by several 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."
Responding to the criticism, Hollande's spokesman recalled this episode.
"Honestly, if Francois Hollande had said to Nicolas Sarkozy 'Get lost, you stupid bastard," he would have had reason to complain," Bernard Cazeneuve said.
"But that's not the kind of thing François Hollande says and François Hollande will not be the president of 'get lost, you stupid bastard'.
"This story is false. François 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 François Hollande 'small' it's meant as a compliment, or that when he calls his supporters 'crackpots' he's just being friendly?"
The alleged epithet caused a storm on Twitter and the comments sections of French news sites, as supporters of both candidates traded insults.
Sarkozy is trailing Hollande in the opinion polls, which suggest that he on course to lose to him in May's second-round presidential run-off, but he has begun making up ground on his rival and observers expect a tight race.