Supporters of Marine Le Pen's National front party are rallying in the streets of Paris.
The far-right party picked up 18% of votes in the first round of France's general election.
Whilst not enough to give Le Pen a serious chance of the winning the election, it has bestowed "kingmaker" status on her as the two leading candidates - Nicolas Sarkozy and François Hollande - vie for the votes of her supporters.
Le Pen has promised to pass judgement on the second round of the election at her traditional May Day rally at the statue of Joan of Arc in Paris later today.
She is expected to call on supporters to abstain from voting rather than endorsing either of her political rivals.
French President Nicolas Sarkozy has appealed directly to far right voters with pledges to get tough on immigration and security, after the National Front's record showing in a first round election made them potential kingmakers.
Mr Sarkozy told reporters outside his campaign headquarters: " National Front voters must be respected. They voiced their view. It was a vote of suffering, a crisis vote. Why insult them?"
The frontrunner in the French presidential elections Francois Hollande has slammed President Nicolas Sarkozy at a campaign rally in Quimper, western France.
Mr Hollande told supporters: "The outgoing candidate, he always succeeds in convincing himself, through others. It reassures him. He does it by himself. And yesterday, he tried to make out what was a failure, to be a success.
"He was happy. He is like that. He also thinks his term was a success. More than 73 percent of the French think the opposite. But he continues to think that he must go on."
Uncertainty in Holland and France has rocked the DOW Jones and the FTSERead the full story ›
The broadcaster France 24 have posted an analysis on their website of how the French press has reacted to the election results.
I am not going to seek out voters from the extreme right, I won't try to seduce them. The far right has strong support at the moment and that's the fault of Nicolas Sarkozy.
But some voters voted for the far right because they're angry (at Sarkozy). They are the voters who I want to hear from.
Francois Hollande's campaign manager said the candidate "wants to offer a dream" to the French people but was aware of the financial constraints that could face them.
He wants to offer a dream, but he doesn't want to sell illusions to the French people.
Undeniably a first step toward change was taken yesterday.