The law allows same-sex couples to wed and adopt children.
A campaign was launched Monday on social media sites by Samuel Lafont, a conservative member of Parliament and a vocal opponent of the law, France 24 reported Wednesday
Writing on Facebook, Lafont said opponents should use the "extraordinary international visibility" of the cycling race to "demonstrate our opposition to this law and to the modern gender theories that lie behind it."
Lafont called the planned multi-day protest the "Tour de France Pour Tous" [Tour de France for everyone], a play on the name of the law, "Marriage Pour Tous."
The Tour de France runs June 29 to July 21, with riders pedaling more than 1,800 miles through the country.