This means that the party has been beaten into third place, despite leading in six of 13 regions in the first round of voting.
Former President, Nicolas Sarkozy’s centre-right republicans are set to win most seats ahead of the ruling socialists.
Acknowledging defeat, FN Leader, Marine Le Pen, pledged to keep fighting. 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 ways by a campaign of lies and disinformation”.
She had stood as a regional presidential candidate in the northern region of Nord-Pas-de-Calais-Picardie, while her niece, Marion Marechal-Le Pen, was the FN’s candidate in the race in Provence-Alpes-Cote d’Azur, in the south.
After both led with more than 40 per cent of the vote in the first round on December 6, the Socialist candidates in those regions pulled out so their voters could support Republican candidates in the second round.
The FN actually increased its votes in the second round to more than 6.8 million, from 6.02 million on December 6 as more people voted, according to the Ministry of Interior (In French). But the FN share of the vote went down slightly from 27.73 per cent to 27.36 per cent.
The Republicans increased their share from 26.65 per cent to 40.63 per cent and the Socialists from 23.12 per cent to 29.14 per cent.
The overall turnout increased from 22.6 million on December 6 to 26.2 million on Sunday. Sunday’s figures were based on a count of 98 per cent of votes so far.