Aix-les-Bains sits on the edge of Lake Bourget in the south-east Rhône-Alpes region and is known for its hot sulphur springs.
Local newspaper Le Dauphiné Libéré reported that a swimmer arrived last Friday at the town's public swimming pool and was told it was closed to the public.
The newspaper reported that the pool has agreed to close at certain times so that male and female pupils from the Tomer-Debora Jewish school can swim at separate times and without members of the public being present.
Under the religious rules the school follows, girls and boys should not swim together.
The pool's policy risks contravening the French principle of secularism, which creates a clear separation of church and state. It is the same principle that has seen headscarves and other religious symbols being banned in schools.
The mayor of the town, Dominique Dord, told the newspaper he was "embarrassed" by the incident, but that the system has been in place since 1977.
"This system has been in operation for 35 years and no other mayor has changed it," he said. "Today, this story is now in the spotlight and I can understand why it's causing a debate."
The mayor said the school pays for the pool to be shut. Other schools are able to use the pool for free but do not request that it is shut to the public while its pupils are in the water.
"This arrangement only applies to ten sessions a year," he said.
The mayor plans to check the legality of the arrangement.
"I am going to ask for legal advice to see whether we are infringing the principle of secularism in the eyes of the law," he said. "If so, then we'll act, but in a cooperative manner. We do not want to stigmatize a community."