Marine Le Pen, the leader of France's National Front (FN), has condemned opponents for colluding to prevent it winning a single region in elections.
Her voters had been "disenfranchised by a campaign of lies", she said.
The FN won 6.8 million votes - its largest ever - but lost in two target regions after the Socialists pulled out and urged supporters to back the conservatives of Nicolas Sarkozy.
Overall, the conservatives took 40.2%, the Socialists 28.9% and the FN 27.1%.
Speaking to supporters after the result became clear, Ms Le Pen said: "You have been disenfranchised in the most indecent of ways by a campaign of lies and disinformation decided in the golden palaces of the Republic and executed in a servile way by those who live off this system and often prosper off the backs of the French people."
But she vowed she would continue the fight, hailing the proportion of votes won.
"Nothing can stop us now," she said.
"In its northern and southern bastions, we've eradicated the evil-doing Socialist Party. By tripling our number of councillors, we will be the main opposition force in most of the regions of France."
Analysis: Hugh Schofield, BBC News, Paris
The main parties are mightily relieved that the political map of France has not been re-drawn.
Despite its triumphant showing in round one of the election, there was no breakthrough for the Front National. But as the full import of the result sinks in, no-one - neither the ruling Socialists nor Nicolas Sarkozy's Republicans - are inclined to celebrate.
They know that the underlying reasons for the far-right's success remain as strong as ever among the white working and lower-middle class.
They are: high unemployment; fear of mass immigration; loathing of Europe and an insurrectionary feeling that targets anything that smacks of the establishment.
Ms Le Pen had fought the northern region of Nord-Pas-de-Calais-Picardie, one of two the Socialists pulled out of.
The other was Provence-Alpes-Cote d'Azur, in the south, contested for the FN by Ms Le Pen's niece, Marion Marechal-Le Pen.
She said: "There are some victories that shame the winners."
Both had led with more than 40% in the first round of voting on 6 December.
Part of the turnaround was also due to an increased nationwide voter turnout, from 50% on 6 December to 58% on Sunday.
Overall, the conservatives took seven regions, the Socialists five, while Corsica went to moderate nationalists.
President Francois Hollande's governing Socialist Party suffered a major defeat in the Paris region, Ile-de-France, which shifted to the Republicans for the first time in nearly 20 years.
Although Mr Sarkozy's centre-right Republicans claimed victory and the Socialists second overall, the BBC's Hugh Schofield in Paris says neither side will be inclined to celebrate.
Mr Sarkozy said the result of the first round had been a "warning sent to all politicians, ourselves included".
Citing unemployment, security and national identity, he said: "We now have to take the time for in-depth debates about what worries the French, who expect strong and precise answers."
Socialist Prime Minister Manuel Valls said: "There is no place for relief or triumphalism... The danger posed by the far right has not gone away, far from it."
These elections were to vote for councils and presidents of the 13 French regions, which have wide powers over local transport, education and economic development.
It was the first electoral test since the 13 November Paris attacks, in which 130 people were killed - an attack claimed by the so-called Islamic State group.
The election was also the last before presidential and parliamentary polls in 2017, and the FN had been hoping to use it as a springboard for Marine Le Pen's presidential bid.
French press: National Front kept in check
- "Relieved, but…" says left-wing daily Liberation. The FN is perhaps France's first party, it says, but for the moment it is only a first-round party
- Centre-left daily Le Monde says the FN was "defeated but also reinforced", while other parties had a "joyless success"
- Conservative Le Figaro says the FN was held in check, and regional daily Ouest-France suggests this was only the "start of a reprieve" for the mainstream parties, given the increase in the FN vote
- La Voix du Nord, which campaigned against Marine Le Pen in the Nord-Pas-de-Calais-Picardie region where she lost, dubs her Republican rival's win a "modest triumph"
- And Var-Matin in the south, where her niece Marion was defeated, says Republican "relief" was tempered by the fact that they "probably only won because the left stepped down"
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