Six weeks after Hollande won the presidency, his fellow Socialists and their political allies were expected to win control of the 577-seat National Assembly in Sunday's second round of legislative elections.
The 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 the outcome will determine the country's political direction, which has Europe-wide importance. France is the second-biggest economy in the eurozone and, along with powerhouse Germany, contributes heavily to bailouts to weaker nations and often drives EU-wide policy.
Coming so soon after Hollande's victory, the parliamentary race has faced the risk of voter fatigue. At 5 p.m. in France, turnout was just under 46.2 per cent on the French mainland — nearly 3-1/2 percentage points fewer than five years ago and slightly less than the figure a decade ago.
The elections come after a hasty new bailout for Spanish banks and on 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, Hollande is pushing for government-sponsored stimulus to encourage growth. That has met opposition from German Chancellor Angela Merkel as the two try to stem Europe's crisis.
Hollande presented other European leaders last week with a new "growth pact" that includes €120 billion ($151 billion) worth of measures around the continent to stimulate growth, French newspaper Journal du Dimanche reported Sunday. The paper said it obtained a copy of an 11-page letter on the issue sent to Merkel and other European counterparts.
Markets have been 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.
In a well-off area of central Paris, voter Eve Baume said she cast her ballot for the local Socialist, Claire Morel, "because I've been waiting for change for a long time. ... Also I wanted to support Francois 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, 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 close in big cities at 8 p.m. (1800GMT). Polling agency projections of the results are expected soon afterward, and 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.
National Front leader Marine Le Pen has revamped the party to try to shed its reputation as racist and anti-Semitic, which was inherited under her father, party founder Jean-Marie Le Pen. Marine Le Pen placed a solid third in the presidential race her party's candidates ranked third in last the first round of the legislative election last week.
But 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.
Angela Charlton and Catherine Gaschka contributed from Paris.Suggest a correction