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

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