President Francois Hollande's Socialists and their allies were on track Monday to win a strong parliamentary majority after a first-round election that cemented France's swing to the left.

A week ahead of a crucial run-off vote, the Socialists and other left-wing parties won about 46 per cent in Sunday's first round ahead of ex-president Nicolas Sarkozy's right-wing UMP party and its allies with 34 per cent, official results showed.

With pollsters predicting the Socialists may win a majority of the National Assembly's 577 seats on their own, party officials on Monday urged voters to keep up the momentum in next Sunday's second round.

"The essential thing is that the president has a strong majority," Socialist Party leader Martine Aubry said.

Sunday's vote also saw a surge in support for Marine Le Pen's far-right National Front, which wants to ditch the euro and battle against what she calls the "Islamisation" of France.

Aubry urged the UMP to withdraw its candidates in constituencies where the far right could win to ensure victory for centrist candidates.

"I call on the UMP to be clear... Many are watching in France and in Europe and I believe we must be clear in defending certain values," she said.

Hollande defeated Sarkozy in last month's presidential election and now wants voters to give him a strong mandate to enact left-wing reforms as France battles Europe's crippling debt crisis, rising joblessness and a stagnant economy.

However, after a high turnout in the presidential election, voters were less enthusiastic on Sunday with participation rate at only 57 per cent, a record low for a first round.

If the second round confirms Sunday's results, it will increase Hollande's status in Europe as champion of the movement away from the German-led fixation on austerity towards growth, and give him a confidence boost in talks with fellow EU leaders this month on the eurozone crisis.

Pollsters say Sunday's results indicate the Socialists will take between 283 and 329 seats in the run-off, likely enough to secure the 289 seats they need to form a majority on their own.

With the 10 to 15 seats expected to go to the Greens, who are close allies of the Socialists and already in government, Hollande is all but certain to enjoy a majority without needing to turn to the Communist-backed Left Front for support.

With the Socialists already in control of the upper house Senate and almost all regional governments, UMP leader Jean-Francois Cope urged voters to balance their power with a swing to the right in the second round.

"All the French men and women who do not want the left to have total power for the next five years must take that decision now," he said.

He also reached out to National Front voters, urging them to switch from the far-right to the UMP to keep the Socialists from victory.

"I am telling the FN's voters: be careful when you vote for the FN in the second round, you risk putting the left in power," Cope said, though he rejected the idea of the UMP forming a second-round alliance with the FN.

At a meeting of its political bureau Monday, the UMP also decided not to overtly call on its supporters to vote against the FN in the 20 constituencies where far-right candidates are facing off against Socialists, party sources said.

The National Front took 13.6 per cent of the vote on Sunday, far above the four percent it achieved in the last parliamentary election in 2007.

"We confirm our position tonight as France's third political force," Le Pen said after the vote.

Still, under France's first-past-the-post system the result would at best give the FN only three parliamentary seats and possibly none at all.

Le Pen said Monday that the party's candidates would stay in the race in all 61 constituencies where they made it to the second round.

Aubry said the Socialists were withdrawing their candidate from the southern Vaucluse area in a bid to prevent the FN's Marion Marechal-Le Pen, the party leader's niece, from winning the seat after she led in the first round.

Sunday also marked a personal victory for Le Pen, who defeated the Left Front's firebrand anti-capitalist Jean-Luc Melenchon in a rundown former mining constituency near the northern city of Lille.

Hollande's interim government has taken a series of popular steps in the wake of his presidential victory in the May 6 run-off.

He has cut ministers' salaries by 30 per cent, vowed to reduce executive pay at state-owned companies and lowered the retirement age from 62 to 60 for some workers.

The UMP has hit back with warnings that the Socialists are preparing huge tax hikes to pay for what the right says is a fiscally irresponsible spending programme.

More than 6,500 candidates competed in Sunday's vote. In races where no candidate won more than 50 per cent of the vote in the first round, any contender who scored more than 12.5 per cent stays in the race for the second round.