However, former presidential candidate Segolene Royal is decrying “political treason” against her after she lost her controversial campaign for a parliamentary seat - quashing her hopes of becoming speaker of the National Assembly.
The defeat deals an embarrassing blow to the Socialist Party, whose hierarchy had backed Royal's candidacy.
Ms. Royal, a prominent Socialist, is President Hollande's ex-partner and the mother of his four children.
Polling agencies say dissident Socialist Olivier Falorni defeated Royal in Sunday's balloting in the western Charente-Maritime region as part of nationwide legislative elections won by Socialists and their allies.
Her campaign became embroiled in controversy last week after Hollande's current companion - journalist Valerie Trierweiler - expressed support for Falorni on Twitter, seen by some as a show of jealousy.
The left was in the spotlight and expected to take the driver's seat of the 577-seat National Assembly after Sunday's second round of legislative elections.
President Hollande's Socialists dominated the first round last week and pollsters predict they will win the most seats in the lower house. That would wrench it from the hands of former president Nicolas Sarkozy's conservatives, who have led it for a decade.
The campaign focused on local issues but will determine the country's political direction, which has Europe-wide importance. France is the second-biggest economy in the euro zone and, along with powerhouse Germany, contributes heavily to bailouts to weaker nations and often drives E.U.-wide policy.
Turnout in the French voting was 21.4 per cent at midday, comparable to the 2002 and 2007 legislative elections, with some voters not bothering to cast ballots because so many were predicting a Socialist victory.
The elections come after a hasty new bailout for Spanish banks, and the same day as crucial voting in Greece. The Greek elections may determine whether the country stays in the euro, with repercussions for all the other 16 countries that use the joint currency.
After budget-tightening in France under Sarkozy that leftists warned would send France back into recession, President Hollande is pushing for government-sponsored stimulus to encourage growth – and has met opposition from German Chancellor Angela Merkel as the two try to stem Europe's crisis.
President Hollande's Socialist government has pledged to reduce the deficit, but markets are worried about higher spending when France's debts are so high.
Hollande, a moderate and mainstream leftist who is committed to European unity, is hoping to get an absolute majority of 289 seats for the Socialists to avoid having to make concessions to the Euro-skeptic far left.
Claire Morel said she voted for the Socialist candidate in her well-off Paris district “because I've been waiting for change for a long time. ... Also I wanted to support François Hollande, the government and its projects.”
Pascal Albe, a voter from the working class Paris suburb of Ivry-sur-Seine, said that though he generally votes for the right, Mr. Hollande should have a Socialist-led parliament. “Otherwise the country will be paralyzed, and especially now, we don't need that,” he said.
Voting stations closed in big cities at 8 p.m. (1800 GMT). Official results are expected late Sunday night.
Political and personal intrigue - and the resurgent far right - have marked the campaign. The anti-immigrant National Front, which wants to abandon the euro and stop immigration, is wrangling for its first real presence in parliament in more than a quarter century.
Sarkozy's conservative UMP party is struggling to hold onto seats, and many candidates are angling for far-right votes.
The French parliament system is such that the party is not expected to get more than three or four seats.
Any candidate who won support of more than 12.5 per cent of registered voters in the first round advanced to Sunday's runoff, and many districts have three-way races. Some 46 million voters are casting ballots for individual candidates at 65,000 voting stations nationwide. Only 36 National Assembly candidates won seats outright in the first round; the remaining 541 seats were up for grabs Sunday.
Intellpuke: You can read this article by Associated Press writer Elaine Ganley, reporting from Paris, France, in context here: www.theglobeandmail.com/news/world/frances-left-wins-parliament-majority-to-back-hollande-polls-say/article4299283/