Hollande seeks parliamentary majority

• The Socialist Party is seeking a majority of parliament's 577 seats
• If the party wins a majority, it would make it easier for Hollande's agenda
• Marine Le Pen's National Front is looking to win its first seats since the 1980s

(CNN) -- French President Francois Hollande looked to solidify his Socialist Party's majority in runoff parliamentary elections Sunday, which would allow him to push through an anti-austerity agenda.

His party is widely expected to win a majority of the 577 parliamentary seats in the second round of voting, though it is unclear whether he can pick up in parliament.

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 will close at 8 p.m., the same time results are expected in Greece elections.

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.

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 America-friendly French presidents in decades.

The president, 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.