PARIS — The French cabinet approved a draft bill legalizing same-sex marriage on Wednesday after weeks of loud opposition, especially from religious figures and the political right.

During his successful campaign for president, François Hollande promised to legalize same-sex marriage. On Wednesday, he said the measure represented “progress for all of society.” Mr. Hollande and his Socialist Party have a majority in both houses of Parliament, and the bill is expected to pass sometime early next year.

The draft law redefines marriage to stipulate that it is “contracted between two persons of different sex or of the same sex,” and the words “father” and “mother” in existing legislation are replaced by “parents.” The bill would also allow married gay couples to adopt children.

Christiane Taubira, the justice minister, told the conservative newspaper La Croix that “marriage for all,” as the government calls it, was a response to “a demand for equality.”