Yves Nicolin, the mayor of Roanne in central France, said on Sunday he was ready to accept refugees in his town - but only if they were Christians.
Roanne could take "maybe a dozen families" but "on condition that they are really Christian refugees who are persecuted because they are Christians in Syria" by the Islamic State armed group, Nicolin told local radio.
That way he could be sure they were not "terrorists in disguise", he said, adding that he also wanted to make certain they weren't "economic migrants".
Nicolin is a member of former president Nicolas Sarkozy's Les Républicains, the mainstream right opposition to Hollande.
Former Sarkozy finance minister, François Baroin, who is mayor of Troyes, east of Paris, on Friday said his city could not take any more asylum-seekers at all.
Troyes' resources are already overstretched, he said, claiming that towns near the capital are most in demand and that France is not in good enough economic and social shape to accept more migrants.
""We can't have Calais everywhere in France," he added, referring to the Channel port where thousands of migrants have gathered, trying to travel to Britain.
Interior Minister Bernard Cazeneuve is to meet mayors who are ready to help the refugees next week, among them Socialists who lead Paris, Lille and Strasbourg but also Républicains, for example from Caen and Saint-Étienne.
Front National (FN) leader Marine Le Pen on Sunday declared immigration a burden and said France does not have the resources to help refugees.
"Immigration is not a stroke of luck, it's a burden," she told cheering supporters at the far-right party's summer school in Marseille this weekend.
"Our country has neither the resources, nor the desire, nor the energy to be more generous with the misery of the world," she said.
She won a standing ovation with a promise to "bring radical Islam to its knees".
Despite his expulsion from the FN and his absence from the meeting, her father, Jean-Marie, approved of her speech, judging it "100 per cent Jean-Mariste".
"So it's difficult to understand why I was expelled," he told France Inter radio.