"I consider it fully correct to make changes to the appropriate documents. It is a current issue and we need to think about it," Putin said at a meeting with lawmakers.
"We need to react to what is going on around us. We respect our partners but ask (that they) respect the cultural traditions and ethical, legal and moral norms of Russia," Putin said, quoted by Russian news agencies.
The Russian parliament, in a law signed by Putin, had already caused a storm last year by banning the adoption of Russian children by American families.
That law was adopted as part of retaliation for human rights legislation adopted by US lawmakers.
The Interfax news agency said Putin's comments on Friday were in response to a question posed by a lawmaker from the western Russian region of Kaliningrad who directly referred to the adoption this month of a bill by the French parliament legalising same-sex marriage.
The lawmaker, named as Marina Orgiyeva, suggested making changes in adoption agreements with France to ensure that Russian children did not fall into the hands of same-sex parents.
Putin did not specify what changes he wanted to see in the agreements.
French President Francois Hollande has promised to sign the gay marriage bill into law as soon as France's Constitutional Council rules on a challenge filed by right-wing lawmakers.
Russia decriminalised homosexuality in 1993 and officially removed it from the list of psychiatric disorders in 1999.
But homophobia remains widespread and socially acceptable, and almost no public figures have come out as gay. Putin prides himself on a virile, heterosexual image.
Several Russian regions have outraged rights campaigners by approving local laws banning gay propaganda among minors, in legislation which is now in the initial stages of discussion at the federal parliament.