French President Francois Hollande looked set to consolidate his grip on power with a left-wing majority in parliament after a first-round vote Sunday, and may be able to govern without relying on hard leftists hostile to closer European integration.

Initial projections by polling agencies based on a partial vote count suggested Hollande's core Socialist bloc could win 283 to 329 seats in the 577-member National Assembly in next Sunday's runoff, shifting the lower house to the left for the first time in a decade, Reuters reported.

With Green allies, the left would have 295 to 347 seats, the CSA polling institute forecast, well ahead of the mainstream conservatives with 210 to 263 seats, and more than the outright majority of 289 needed to give Hollande a free hand.

According to preliminary figures from the Ipsos polling agency reported by France 24, the Socialsts and their allies secured 47.1 percent of the votes in the first round of France's parliamentary elections on Sunday while ex-President Nicolas Sarkozy's UMP and its right-wing allies garnered 35.4 percent. 

The far-right National Front took 13.4 percent of the vote, less than its leader Marine Le Pen's 17.9 percent presidential score, and is projected to have at most three deputies. The anti-immigration party will be present in fewer runoffs than it had hoped due to the low turnout.

Nevertheless, Le Pen herself bested hard leftist Jean-Luc Melenchon in Henin-Beaumont in the northern Calais region, and a Socialist candidate may pip the Left Party leader for second place on the ballot for round two.

In another closely watched race, Hollande's former partner Segolene Royal, who ran for president in 2007, was narrowly ahead of a maverick leftist rival in the western seaside town of La Rochelle and faces a difficult three-way runoff.

The parliamentary balance is hard to predict accurately because any candidate winning more than 12.5 percent of registered voters can go through to the June 17 second round, meaning three candidates may face off in many constituencies. 

With the Senate already under the control of the Socialists, a majority in the lower house would give Hollande unprecedented power to force through his reform programme.

Turnout was 48.31 percent at 5 p.m. (11 a.m. EDT), three hours before the polls closed, down from 49.28 percent in the 2007 parliamentary vote, Reuters reported. Abstention rates have soared since France synchronized the presidential and parliamentary terms a decade ago, hitting 40 percent in 2007.