The lower house National Assembly began its second reading of the bill late Wednesday and was to give its final approval on April 23, under a fast-track measure that limited debate to 25 hours.
Opposition to the bill has failed to die down, despite it being approved by the Senate last week, with critics vowing mass protests to derail the proposition.
Some 2,700 opponents gathered in Versailles outside Paris late Tuesday to protest the bill, leading to scuffles with police. Opponents have vowed new mass demonstrations in the next week.
"These protests have a right to take place, we are in a republic. But calls for violence, calls to hate, must be condemned," Ayrault told journalists, urging right-wing politicians to "call for calm" among supporters.
The bill has proved hugely controversial in a country that is officially secular but predominantly Catholic, mobilising hundreds of thousands of people for months in pro- and anti-gay marriage protests nationwide, some violent.
A mass protest in Paris is also planned for May 26 if the law is approved, to demand its withdrawal and a referendum on gay marriage.
Introducing the bill for its second reading, Justice Minister Christiane Taubira decried "spouters of hatred" who had violently opposed it.
"This bill takes nothing away from them -- there is more than one way to live as a couple or as a family," she told the assembly.