Paris (CNN) -- French President Francois Hollande was looking to solidify a Socialist majority in runoff parliamentary elections Sunday, which would allow him to push through an anti-austerity agenda.
Socialists are widely expected to win a majority of the 577 parliamentary seats in the second round of voting. Exit poll projections show the Socialists and their supporters likely won about 320 seats, with the center-right UMP (Union for a Popular Movement) party winning 221, the extreme left Left Front with 10 and the centrist MODEM winning two seats.
More than 500 seats will be decided in the latest round of balloting, according to French election officials, after candidates failed to receive a majority of votes cast in their districts as well as 25% percent of registered voters in their district.
Polls opened at 8 a.m. (2 a.m. ET) and closed at 8 p.m.
If the Socialists cannot get a majority, Hollande will have to rely on support from other parties for his agenda.
Election observers are keeping an eye on challenges by Marine Le Pen and her conservative National Front, the third-largest political party in France.
The National Front, which has gained in popularity in France thanks in large part to its anti-immigration platform, is battling to fill a few parliamentary seats for the first time since the 1980s. Exit poll projections showed the party likely won two seats.
Le Pen made a failed bid for president against Hollande and then-President Nicolas Sarkozy.
Hollande has unsettled investors with his criticism of the austerity policies central to European bailout deals for troubled economies such as Greece's and Ireland's.
His policies have put him at odds with Germany's Angela Merkel, who holds the purse strings for a large portion of the European Union's bailout efforts.
Hollande became France's first Socialist president since François Mitterrand left office in 1995 as he swept to election victory over the incumbent Sarkozy, one of the most U.S.-friendly French presidents in decades.
Public opinion polls indicate that Sarkozy's right-wing majority may lose between 75 and 100 parliamentary seats.
Hollande, who was sworn into office in May, has chosen mostly moderates for his Cabinet, indicating an effort to build a broad coalition in the country.
Last month, Hollande said he wants to balance the need to reduce the debts of European governments with efforts to stimulate growth.
CNN's Jim Bittermann contributed to this report.