The triumphant leader of the far-right National Front (FN), Marine Le Pen, says French voters rejected the "old political class" in regional elections that put her party top.
Nearly one-third of voters backed the anti-immigration FN, which won in six out of France's 13 regions.
Despite the FN surge, a second round on 13 December will be the decider.
It was the first electoral test since last month's Paris attacks, in which jihadist gunmen killed 130 people.
The nationalist FN got about 28%, ahead of the centre-right Republicans party led by former President Nicolas Sarkozy, which polled just under 27%, and the governing Socialist Party (PS), trailing with 23.5%.
The PS said it was withdrawing from the second round in two regions, in the north and south, to try to block a run-off victory for the FN.
On Twitter, Marine Le Pen said both the PS and Republicans "are crumbling" and "the French people are sick and tired of that old political world".
In a series of interviews she condemned the PS for withdrawing some candidates from the second round, saying the PS was "neither loyal nor democratic" and was "treating its voters like ballot fodder".
The PS candidate in a third region, Alsace-Champagne-Ardenne-Lorraine in eastern France, rejected a call from party leader Jean-Christophe Cambadelis to withdraw in the second round. Jean-Pierre Masseret said he could not be expected to leave 5.5 million people in the hands of a Republican party that had veered to the extreme or an extreme nationalist right.
Mr Sarkozy refused to do any tactical deals with the PS for the second-round ballot.
The result on Sunday was a major blow for Socialist President Francois Hollande, who had seen improved poll ratings after the Paris attacks.
‘First party of France'
France's new regional authorities have wide powers over local transport, education and economic development.
The vote is also an important test of FN support ahead of the 2017 presidential election.