There were more than 6,500 candidates vying for the 577 seats in the lower house of the National Assembly, Radio France International said.
Hollande, elected last month, is the left-wing leader who beat out former rightist President Nicolas Sarkozy. Hollande has a "tax and spend" agenda that will require parliamentary support to get the stagnant economy and high unemployment reined in, RFI said.
As for the opposition, Sarkozy's conservative UMP party is without a leader and euronews.net said that's created some confusion among past supporters who are uncertain as to the party's direction.
The far-right, anti-immigration Front National party led by Marine Le Pen was also hoping to make parliamentary inroads after she won 18 percent of the vote in last month's first round of the presidential voting, RFI said.
The second round of parliamentary voting takes place next Sunday.