France's far-right National Front (FN) appears to have made big gains in the first round of regional elections, estimates show.
They put the FN ahead in at least six of 13 regions in mainland France.
The elections are the first electoral test since last month's Paris attacks, in which 130 people were killed.
The centre-right Republicans party led by former President Nicolas Sarkozy appeared to be in second place ahead of the governing Socialist Party.
A second round of voting will be held on 13 December.
As the results became clear, the Socialist party said it was withdrawing from the second round in at least two regions, in the north and the south, to try to block a run-off victory for the FN.
Exit polls from Sunday's vote predicted that the FN had won 30.8% of the vote, followed by Mr Sarkozy's Republicans on 27.2% and President Francois Hollande's Socialists with 22.7%.
FN leader Marine Le Pen, who stood in the northern region of Nord-Pas-de-Calais-Picardie, and her niece Marion Marechal-Le Pen, who stood in Provence-Alpes-Cote d'Azur in the south, both looked to have won more than 40% of the vote, polls predicted, breaking previous records for the party.
Marine Le Pen told supporters it was a "magnificent result" which proved the FN was "without contest the first party of France".
Analysis: Hugh Schofield, BBC News, Paris
The message from the first round of France's regional elections is simple and unequivocal - once again the far right has come out on top.
For the third time in a year and a half, Marine Le Pen can legitimately say that her National Front is the country's most popular party.
It is an astonishing performance for a party that until very recently was regarded as beyond the pale.
The Paris attacks will have played a part in this but it would be wrong to ascribe Ms Le Pen's triumph solely to fears of terrorism.
Her party has been on a steady upward slope for four years. The problems that worry voters are as much economic and social as they are security-related.
In previous years, the centre-right opposition and governing Socialist party have worked together to block the FN.
However, Mr Sarkozy said there would be no "tactical alliances" in the second round.
French regions have wide powers over local transport, education and economic development.
The BBC's Lucy Williamson, in Paris, says the far right has been steadily gaining votes over the past few years from both left- and right-wing sympathisers through a mix of nationalist and pro-welfare policies.
In the lead-up to the election, opinion polls suggested that the popularity of the anti-immigration, anti-EU National Front had increased since the attacks on 13 November.
The election has been held under a state of emergency declared after the Paris attacks, which were claimed by Islamic State militants.
The FN is hoping a strong performance will boost Marine Le Pen's chances for the 2017 presidential election.
The government's response to the Paris attacks has boosted President Hollande's approval ratings - they have soared more than 30 percentage points to 50%.
However, this surge in personal popularity has so far not translated into greater approval for Mr Hollande's Socialist Party, which is trailing with about 22%.
Prime Minister Manuel Valls made an "appeal to patriotism" on Thursday in an effort to rally the Socialist vote.
Assemblies are being elected in the 13 regions of metropolitan France and in four overseas territories.
Suspects at large
On Friday, the Belgian prosecutor's office said police were seeking two new suspects accused of aiding the fugitive suspect from the Paris attacks Salah Abdeslam, who lived in Belgium.
The pair are "armed and dangerous" and are thought to have helped Abdeslam travel to Hungary in September.
Investigators say Abdeslam may have driven the suicide bombers at the Stade de France to their target on the night of the Paris attacks.
But Abdeslam's precise role in the attacks remains unclear. There are suggestions he was meant to carry out a suicide attack on the night but decided against it.