Five weeks after the Socialist Party's Francois Hollande scored a victory in France's presidential election, public-opinion polls show his fellow party members may soon win either a plurality or even a majority of the seats in the lower house of the country's Parliament.

All 577 seats in France's National Assembly are at stake in the two rounds of elections beginning Sunday and ending June 17, with control going to the bloc or party with a majority of 289 seats.

The Socialists are already members of the majority coalition in the upper house of the country's Parliament (i.e., the 331-seat Senate).

Control of the National Assembly is important to Hollande because the history of the French Fifth Republic has shown a president on either side of the aisle without a majority there can run into trouble from time to time (e.g., the left-of-center Francois Mitterand, the right-of-center Jacques Chirac).

One set of three recent polls conducted by Ifop, OpinionWay, and TNS Sofres indicate a bloc headed by the Socialist Party could control between 271 and 334 seats in the National Assembly, according to Bloomberg News.

Another set of three recent polls conducted by BVA, Ipsos, and Harris Interactive suggest similar results, with the Socialist Party seeming a bit short of attaining a 289-seat majority on its own, Reuters reported.

The Socialist Party anticipates it may be able to form a governing coalition with the Europe Ecology-The Greens party, the Christian Science Monitor said.

However, the Socialist Party may require at least one other coalition partner, such as the Radical Party.

Even if the Socialists do win a majority, it could be with such a tight margin that Hollande won't be able to rule without allies, Adelaide Zulfikarpasic, head of the opinion department at pollster LH2, told Bloomberg. The question then becomes what conditions the far left imposes as a price.

Members of the National Assembly chosen by voters in the last election in 2007 included 313 from the right-of-center Union for a Popular Movement, or UMP (led by former President Nicolas Sarkozy), 186 from the left-of-center Socialist Party, and 22 from the New Center party, according to the International Foundation for Electoral Systems' ElectionGuide.

In the elections to get under way within hours, the ElectionGuide noted:

--  A candidate will be elected in the first round if he or she obtains an absolute majority of the total votes cast, provided the figure is equal to or greater than one-quarter of the number of registered voters in the particular constituency.

--  A candidate is eligible for the second round if he or she obtains in the first round a number of votes equal to at least 12.5 percent of the number of registered voters in the particular constituency. If only one candidate fulfills this condition, however, then the person who polls the second-highest number of votes in the first round may also participate in the second round, when a simple majority will suffice to win the election.

France has an estimated 65.63 million population, and the country has an estimated 46.07 million registered voters.