PARIS — French President Francois Hollande has signed a law authorizing gay marriage and adoption by same-sex couples, after months of nationwide protests and wrenching debate.

His signature means the first gay marriages may be celebrated in France within about 10 days. Hollande's office said he signed the bill Saturday morning, a day after the Constitutional Council struck down a challenge to the law.

Hollande, a Socialist, had made legalizing gay marriage one of his campaign pledges last year. While polls for years have shown majority support for gay marriage in France, adoption by same-sex couples is more controversial. The bill prompted months of widespread protests, largely by conservative and religious groups. Some were marred by clashes with police. It became a flashpoint for frustrations at the increasingly unpopular Hollande.