The National Front failed to build on first-round leads in the French local elections and has not won any regions.

Marine Le Pen's far-right group gained more votes nationally than any other party in last week's first round, boosted by the migration crisis and the Paris terror attacks.

But after the final stage of voting it appears Nicolas Sarkozy's conservatives and their centre-right allies are the big winners with six of the 13 regions, the Interior Ministry said.

The result for the Paris region is not in, but pollsters predict the conservatives have also won there.

With most of the votes counted, the governing Socialists appear to have secured five regions, while the winner in Corsica is not affiliated with a major party.

Both Ms Le Pen and niece Marion Marechal-Le Pen have lost in their respective regions after the Socialists withdrew and urged supporters to back the conservatives.

Even so, the National Front is projected to have gained many individual seats.

"Nothing will stop us," Ms Le Pen told cheering supporters in northern France.

"By tripling our number of councillors, we will be the main opposition force in most of the regions of France."

She also celebrated the "total eradication" of the left, who dropped from 12 to five regions.

Socialist Prime Minister Manuel Valls responded to the exit polls by saying: "Tonight, there is no place for relief or triumphalism. The danger posed by the far-right has not gone away, far from it."

The vote has been viewed as key for all three 2017 hopefuls: Ms Le Pen, Socialist President Francois Hollande, and former president Mr Sarkozy.

It is Mr Sarkozy who appears to have had the best night and he paid "homage" to the voters who helped record an increased turnout of 58%.

But he too hinted at the need to take the National Front vote share seriously.

"We are proud ... of the results," he told supporters of his Republicans party. "(But) we must now take the time to debate the fundamentals of great questions that are anguishing the French."

Definitive results are expected on Monday.

The regional councils in France are responsible for education, public transport and other administrative sectors.