Marine Le Pen, France's far-right National Front political party leader, gestures as she delivers a speech after the second round in the French mayoral elections in Nanterre, March 30, 2014. [Photo/Agencies]

"This is the price of the brave reforms that have been undertaken," Finance Minister Pierre Moscovici said of pension reforms and tax hikes brought in by Hollande in a bid to narrow France's public deficit.

"We cannot, and we shall not, remain deaf to the message the French have sent us," he told national television.

"There have been huge losses, a drubbing, for the candidates backed by the government," said Alain Juppe, the conservative mayor in the southwest city of Bordeaux who already won a new mandate in last week's first round.

But the FN failed to win the southern town of Avignon as it hoped, and was unlikely to secure the eastern town of Forbach, another of its key targets.

RECORD LOW TURNOUT

Sunday's runoff round of voting came after a week that saw French unemployment surge to a new record. A record 38.5 percent of voters chose to abstain, a fact pollsters said played into the hands of the FN.

Some 80 percent of the French want him to dismiss Prime Minister Jean-Marc Ayrault, according to a Harris Interactive poll this week, and ambitious and tough-talking Interior Minister Manuel Valls is their favourite to replace him. Veteran Foreign Minister Laurent Fabius is also seen a contender.

Pollsters had identified half a dozen FN-run towns emerging after the vote, giving the party a chance to try exercising power once more. Its attempts to run the three southern towns it won in 1995 and a fourth it won in a 1997 by-election backfired as it showed a lack of competence in power.

Despite the election losses, Hollande's government has said it will stick with economic reforms and spending cuts, including a plan to phase out 30 billion euros ($41 billion) in payroll tax on companies in exchange for hiring more workers.

A government source said Paris was preparing tax breaks for households, which would raise questions over whether France can fulfil a promise of bringing its public deficit down below the European Union target of 3 percent of gross domestic product.