Béziers mayor Robert Ménard, an independent elected mayor with the support of Marine Le Pen's Front National, was questioned by police in Montpélier for over an hour on Wednesday, following an outburst on French TV that has caused a political storm.
On Monday evening he told France 2 TV that his administration had used lists of pupils’ names to establish that 64.6 per cent of pupils in the town’s schools are Muslim.
"I know I don't have the right to do it," he said. "Excuse me for saying so but first names are an indicator of religion. To say otherwise is to deny the obvious."
Under French law the authorities are not allowed to keep statistics on people’s religion or ethnic origins and anyone else wishing to compile them may only do so with the subjects' consent.
On Tuesday he was condemned by politicians of both left and right and civil liberties and human rights organisations joined in the outcry.
A statement was then issued from the mayor’s office in Béziers denying that there was any list of children’s names or that any effort had been made to identify which were Muslim.
Police raided the town hall on Tuesday as part of their investigation and Ménard was summoned to explain himself to th authorities.
The row rumbled on on Wednesday.
The mainstream right mayor of the northern town of Tourcoing, Gérald Darmarin, called on Prime Minister Manuel Valls to suspend Ménard.
Valls himself earlier tweeted "Shame on the mayor".
"To keep files on children is the first step to identity politics," Laurent Wauquiez, the general secretary of Darmarin's UMP, told RMC radio, although he said he was open to the idea of polls that would establish "the sociological reality of your population".
Hard-left leader Jean-Luc Mélenchon declared himself "horrified".
"They're keeping files on children, people have gone mad," he told RMC.