France is holding the first round of parliamentary elections Sunday, a vote which will ultimately determine the pace of reform under the country's new Socialist President Francois Hollande.

Opinion polls show that leftist parties could gain a slim majority of the 577 seats in the National Assembly, the lower house of parliament.

But, it is not clear whether the Socialists and their allies will win the necessary solid majority in the first round against the conservative UMP party, led by former president Nicolas Sarkozy.

Analysts say that working with Greens and their hard-left allies, Mr. Hollande, who took power last month, could cobble together a majority to enact measures he hopes will help curb unemployment and jump-start Europe's second largest economy.

Marine Le Pen's far-right National Front is seeking to win a voice in parliament for the first time since the 1980s, after she placed third in the presidential race.

Early returns are expected after polling stations close Sunday evening. A second and final round of voting is scheduled for June 17.

France's Senate, the upper house of parliament, is already under left-wing control.

Mr. Hollande unseated Mr. Sarkozy in a May 6 runoff election. The new president needs lawmakers' support to persuade European Union leaders, especially German Chancellor Angela Merkel, to focus on spurring economic growth rather than enforcing austerity in struggling European economies.

France has about 45 million eligible voters. Those living in remote overseas territories, such as French Guyana, French Polynesia and the Caribbean islands of Martinique and Guadeloupe, began voting Saturday.