Thursday, 08 Nov 2012, 04:51
The bill, opposed by more than 1,000 mayors and the Catholic Church, will be debated by parliament in January.
France already allows civil unions between same-sex couples, but it was a campaign pledge of President Francois Hollande to extend their rights.
It is one of the most divisive issues he has faced, correspondents say.
Mr Hollande told his cabinet that the bill would mean "progress not only for individuals but for the whole of society".
But at the weekend the head of the French Council of Bishops, Cardinal Andre Vingt-Trois, described gay marriage as "the ultimate deceit".
And an opposition senator in the conservative UMP, Serge Dassault, said: "It's the end of the family, the end of children's development, the end of education - it's an enormous danger to the nation."
More than 1,000 mayors have signed a petition against the proposed changes, there have been protests in 75 towns and cities, and one opposition politician has even suggested that legalising gay marriage could lead to polygamy, says the BBC's Maddy Savage in Paris.
Some in the government argue that the law should go even further by offering state funding for artificial insemination for gay couples.
At present only married couples - not civil union partners - can adopt in France.
A number of European nations, including Germany, Sweden and the UK, already allow gay adoption.
Source: BBC News