Same sex marriage is illegal in France, although Socialist presidential candidate François Hollande has made changing the law one of his manifesto promises if he is elected.
The communist mayor of the town, Claudine Cordillot, hopes the symbolic marriage will help advance the cause of same sex marriage in France.
In January 2011, the country's highest authority on the constitution, the Conseil Constitutionnel, ruled that "marriage is the union of a man and a woman."
The issue was brought to parliament in June 2011 but MPs voted against a proposal to change the law by 293 votes to 222.
An opinion poll for Le Parisien newspaper in January found that 63 percent of French people are in favour of granting marriage rights to same sex couples.
There are still strong voices against the proposal in France, with at least one candidate for the presidency, Christine Boutin of the christian-democratic party, firmly against.