France has become the 14th country worldwide and the ninth in Europe to legalise same-sex marriage after a vote in the French Parliament on Tuesday.
The law also makes it possible for the first time for people to adopt regardless of their sexual orientation.
Anglican Mainstream said the outcome would be a source of "regret" for many Christians.
Same-sex marriage was voted in by 331 votes to 225 following months of protests and heated debate between supporters and opponents.
Opposition has sometimes been violent, with a reported increase in attacks on gay people and gay establishments.
As the debate was taking place in the parliament, riot police were stationed outside to keep the peace.
Similar legislation is making its way through Parliament in the UK. Despite the outcome in France, Anglican Mainstream said it was not inevitable that it would be passed here. It is encouraging Christians to write to MPs about their concerns.
In a statement it said: "Many Christians will regret the outcome of the vote for 'same-sex marriage' in the French Parliament, which highlights concerns about news management in the mainstream media in Western societies.
"It should not be assumed that the vote in the UK Parliament will go the same way. The key issue is how marriage as traditionally understood – a lifelong, exclusive commitment between a man and woman – contributes so significantly to the flourishing of human society.
"Although this matter is of particular significance to Christians (and people of other faiths), its ramifications extend into society as a whole: for example, its implications for what teachers will be required to teach children about same sex practice."