The bill - which was approved with only minor amendments - is now certain to become law after a final vote in the lower house, expected in May.
There have been several demonstrations in Paris both for and against the bill.
Gay rights organisations say homosexuals are being increasingly targeted amid opposition to government plans to give gay couples in France the right to marry and adopt children.
Friday's Senate vote, by a show of hands, came after senators had on Wednesday approved the first article of the bill allowing gay couples to marry and adopt, by 179 votes to 157.
Justice Minister Christiane Taubira praised the result, saying the Senate had strengthened French society "by granting the simple recognition of full citizenship to homosexual couples".
The bill is now set to become law after technical second readings in both houses of parliament.
Protesters hold a rally in Paris against critics of a gay marriage bill, claiming they are homophobic Activists say there has been a rapid rise in homophobic assaults in recent months
On Thursday, some 5,000 people took part in a protest in Paris linking critics of the gay marriage bill to homophobia.
The rally came as an image apparently showing the victim of a homophobic attack went viral on social media.
Opponents of the bill have denied homophobia and denounced violence.
Opinion polls suggest that around 55-60% of French people support gay marriage, but only about 50% approve of gay adoption.
The anti-gay marriage lobby, backed by the Catholic Church and right-wing opposition, has already held large marches in Paris.
It argues the move would undermine an essential building block of society.
