France is holding the second round of regional elections in which the far-right National Front (FN) is seeking to consolidate its gains from a week ago.
Marine Le Pen's FN is leading in six of 13 regions in mainland France.
But opinion polls indicate that the centre-right Republican opposition of Nicolas Sarkozy has gained ground since then.
The Republicans pushed the ruling Socialists into third place in the first round.
The Socialists have removed losing candidates from vulnerable seats to avoid splitting the anti-FN vote. However, the Republicans have refused to do the same.
The second round of France's elections have traditionally acted as a brake on the FN, the BBC's Lucy Williamson in Paris reports.
But in some areas the results of Sunday's vote are expected to be close, and these elections are being watched for signs of what position the FN now occupies in French politics, our correspondent says.
The FN won 27.73% of the vote in the first round, followed by Mr Sarkozy's Republicans on 26.65% and President Francois Hollande's Socialists with 23.12%.
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.
Marine Le Pen later told her supporters it was a "magnificent result" which proved the FN was "without contest the first party of France".
As well as those two regions, the vote in Alsace-Champagne-Ardenne-Lorraine is being closely watched. There, the Socialist candidate rejected his party's call to pull out.
French regions have wide powers over local transport, education and economic development.
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, correspondents say.
In the lead-up to the first round, opinion polls suggested that the popularity of the anti-immigration, anti-EU FN had increased since the deadly attacks in Paris on 13 November.
The FN is hoping a strong performance will boost Marine Le Pen's chances in 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.