The formal vote came 10 days after lawmakers voted overwhelmingly in favour of its key article which redefines marriage as a contract between two people rather than between a man and a woman.
The Senate, the upper house of parliament, will debate the law from April 2.
Gay marriage has proved to be a highly divisive issue in officially secular but overwhelmingly Catholic France, with hundreds of thousands taking part in protest marches.
The anti-gay lobby is set to stage a new march on March 24.
Opinion polls suggest a clear majority of French voters support the right of gay couples to wed and a narrower majority favour them being granted the right to adopt as couples.
Gay men and women can already adopt as individuals if approved by social services.
A separate law on providing medically assisted conception to gay couples, already extended to heterosexual couples unable to conceive, will be debated later in the year.