French overseas departments began voting on Saturday, ahead of Sunday's poll in France itself
French people are voting in parliamentary elections expected to determine the extent and pace of reform under new President Francois Hollande, reports the BBC.
Voting for the lower house is beginning with a first round, followed by run-offs a week later.
Correspondents say if Hollande's Socialist Party can win a majority, he will have the mandate to push through bold tax and spend policies.
There is also a closely watched battle between the far right and the far left.
The far-right National Front is hoping to follow up a strong performance in the recent presidential election by gaining its first presence in the 577-seat National Assembly since the 1980s.
The BBC's Christian Fraser, in Paris, says that with the senate already under the control of the Socialists, a majority in the lower house would give Francois Hollande unprecedented power to force through his reform programme.
Hollande's government is due to present a revised budget plan to parliament next month.
The result of the parliamentary election will determine the pace of reform and how radical it becomes, our correspondent says.
If the left fails to win, France would enter into a period of "cohabitation", in which the presidency and the lower house are controlled by political rivals.
The right-wing Union for a Popular Movement (UMP) - the party of former President Nicolas Sarkozy - is defending an absolute majority in the current National Assembly.
The party has concluded an electoral agreement with its centrist Radical Party and New Centre allies.
With the parliamentary polls coming hot on the heels of April's presidential election, there have been concerns over voter turnout.
Speaking on Thursday, Hollande said: "I call on the French to vote. I call on them to give a large majority, a solid and coherent one."
One of the main stories of the presidential election was the third place finish of the National Front's Marine Le Pen.
The far right's strongest chances of success in this poll are in a string of constituencies in the north and southeast, our correspondent says.
The key battle is in the northern industrial town of Henin Beaumont where Ms Le Pen faces the flamboyant leader of the far left, Jean Luc Melenchon.