Early results suggest the party has been beaten into third place, despite leading in six of 13 regions in the first round of votes a week ago.
The polls predict Nicolas Sarkozy's centre-right Republicans will win most seats ahead of the ruling Socialists.
Acknowledging defeat, FN leader Marine Le Pen pledged to keep fighting.
And she blamed the outcome on the mainstream parties which joined forces to keep the FN from power, telling her supporters they had been "disenfranchised in the most indecent of ways by a campaign of lies and disinformation". (+ video) » | Sunday, December 13, 2015
