A gay couple in southwestern France on Wednesday filed a criminal complaint against a mayor who refused to wed them in defiance of a landmark law, one of a small band of diehards holding out against same-sex marriages.

Jean-Michel Colo, the mayor of Arcangues, stirred up controversy by becoming the first French official to formally refuse to marry a gay couple -- Jean-Michel Martin and Guy Martineau-Espel -- and then making several combative statements.

Isabelle Duguet, the couple's lawyer, said she had filed a complaint against Colo for discrimination and refusal to carry out his official duties. The 60-year-old has been mayor of Arcangues for three decades.

Duguet said he could face a five-year jail term and a 75,000-euro ($98,000) fine and described her clients' situation as "intolerable, especially unjust, degrading and discriminatory".

Defending his stand, Colo said earlier: "For me, marriage is for a woman and man to have children. I am not discriminating as a same-sex couple is sterile. It's a parody of equality, it's a big lie."

"I will go to the gallows" rather than back down, Colo said.

Jean-Yves Clouet, the mayor of the small town of Mesanger in northwestern France, has also voiced his defiance, saying: "I have my convictions and I will not carry out these kind of marriages, that's for sure."

But Clouet said he would not have any problems if one of his deputies officiated, adding: "If this law had existed in 2008, I would not have been a mayoral candidate."

In April, France became the 14th country to legalise same-sex marriage after President Francois Hollande, who had made the issue a major electoral plank, signed the measure into law following months of bitter political debate.

The first gay marriage in France was held on May 29.

Martin said he and his partner had offered a compromise solution to the Arcangues mayor but were spurned.

"Our initial aim was to create the least waves possible, without any publicity or media presence," Martin said.

"To respect his beliefs, we even told him that we were ready to get married not in the town hall but in our home in the presence of a magistrate but he refused this too."

The couple, who have been living since 2003 in Arcangues -- a small commune of 3,000 residents -- say they want to get married to ensure pension and inheritance rights.

"It is now time to turn to the law," said Martineau-Espel. "We had been ready to make concessions earlier, now we want the marriage to be held at the town hall."

Interior Minister Manuel Valls warned Colo of "significant sanctions", telling reporters that any public servants refusing to respect the law would be guilty of discrimination and thus risk up to three years in prison, as well as paying 45,000 euros in damages.

Colo's stand has been applauded by the likes of Serge Harismendy, who heads the local chapter of the anti-gay marriage movement "Manif pour tous." He said Colo had "dared to confront threats and pressure".

Opposition to the legislation started as a grassroots campaign which was backed by the Roman Catholic church.

The right-wing opposition then jumped into the fray and the movement ballooned in the run-up to the passing of the law.