France's Socialists won control of parliament Sunday, handing President Francois Hollande the convincing majority he needs to push through his tax-and-spend agenda to battle the eurozone debt crisis.

The Socialists' bloc obtained between 308 and 320 seats -- an absolute majority in the 577-seat National Assembly -- and so will not need to rely on the Greens or the far left, polling institutes CSA, Ipsos and Sofres said.

The far-right National Front was set to return to parliament for the first time since 1998 after winning at least two seats in the south of the country, although party leader Marine Le Pen lost her own bid for a seat.

Hollande, who defeated right-winger Nicolas Sarkozy in a May presidential election, had urged voters to give him the MPs he needs to steer France through the eurozone crisis, rising unemployment and a faltering economy.

"The task before us is immense," Hollande's Prime Minister Jean-Marc Ayrault said as results came in from the run-off vote. "Nothing will be easy."

Beyond Hollande's election promises of job creation and tax hikes, the government will have to pass unpopular measures to bring the deficit below three percent of GDP, with no sign of the eurozone's debt crisis improving.

Sarkozy's UMP and the New Centre won between 221 and 231 seats, the Socialist-allied Greens 20 seats and the far-left Left Front 10, the polling institutes said, with the centrist MoDem winning two seats.

While Le Pen's anti-immigrant and anti-EU National Front (FN) was set to return two to four MPs to parliament, she will not be among them.

Le Pen, who has said her success in the first-round parliamentary vote made her party France's "third political force", demanded a recount after she was narrowly defeated by a Socialist in a northern former mining constituency.

But the telegenic Le Pen nevertheless rejoiced in the overall success of her party, whose image she has fought to soften from the days of her father Jean-Marie's provocative outbursts.

"This is an enormous success," Marine Le Pen said in Henin-Beaumont.

"We only have reasons to be happy to have achieved spectacular results in dozens of constituencies in the second round."

Le Pen's niece, 22-year-old Marion Marechal-Le Pen, won her seat in the southern Vaucluse region and the FN won another seat in the nearby Gard constituency.

The media spotlight was also focused on Segolene Royal, Hollande's former partner and mother of their four children, who conceded defeat in her battle after a dissident Socialist candidate refused to stand down.

Royal, whose campaign was shaken when Hollande's current partner Valerie Trierweiler tweeted her support for dissident Olivier Falorni, slammed what she called a "political betrayal".

"I ran a tough but straight and loyal campaign," she said in bitter but brief remarks in La Rochelle in western France.

While some commentators predicted the end of Royal's political career, the 2007 presidential candidate beaten by Sarkozy said she planned to "continue to have an impact on national policy decisions."

The Socialists and allies won 50.34 percent of votes overall, interior ministry figures said, almost as high as the record 54 percent won shortly after Francois Mitterrand became France's last Socialist president in 1981.

As result estimates came in, UMP leader Jean-Francois Cope said he "took note of the left's victory" and said his party would constitute a "responsible and vigilant opposition."

"I solemnly call for the unity of our political family," Cope said, saying a party leadership election would be held in November.

With the French voting for the fourth time in eight weeks after electing their first Socialist president in 17 years, turnout was a record low for a second-round parliamentary vote at 56 percent.

Already in control of the Senate and nearly all regional governments, the parliamentary majority gives the Socialists a free hand to implement reforms after the right urged voters to check the left's power in the polls.

Hollande heads to Mexico for G20 talks on Monday flush with electoral success and brandishing a further mandate to push for growth strategies -- rather than austerity measures -- to battle the eurozone's debt crisis.

He has also floated a proposal for a 120 billion euro ($150 billion) "growth pact" to be discussed at a series of high-level meetings ahead of a European Union summit on June 28-29 in Brussels.