French President Francois Hollande arrives for a press conference in Brussels on May 24, 2012.

Story highlights

Candidates could head to a runoff vote June 17

If the Socialist Party wins a majority, it would help new president Hollande's agenda

Hollande has chosen mostly moderates for his Cabinet

CNN  — 

Authorities were tallying results Sunday in France’s parliamentary elections, a key vote that could determine whether the country’s new president can push through his agenda.

Voters cast ballots across France to fill 577 parliamentary seats. If President Francois Hollande’s Socialist Party wins a majority, it will be easier for him to garner support for his proposals.

Hollande has been critical of the austerity policies central to European bailout deals for troubled economies there.

To win the first round of voting, parliamentary candidates must receive a majority of votes cast in their districts as well as enough votes to represent 25% of all registered voters in their districts. If those requirements aren’t met, candidates will head to a runoff vote, scheduled for June 17.

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

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..

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.

CNN’s Claudia Dominguez and Ben Brumfield contributed to this report.