The women, from the Citizen Alliance of Grenoble, were told they weren't allowed the swimsuits at the complex.
Police later questioned them and they were fined €35 (NZ$60), local media reported.
The protest comes as a week-long heat wave begins across Europe. Grenoble reached temperatures between 34C and 40C until at least Monday.
"We have a dream: to have fun in public swimming pools like all other citizens, to accompany our children whenever they want to have a swim while it is very hot in the summer here in Grenoble," said two Muslim women, Hassiba and Latifa.
France, Belgium, the Netherlands, Bulgaria and the German state of Bavaria have all imposed some restrictions on the wearing of full-face veils in public places.
"We must fight against discriminatory policies and prejudice in France, as we are actually deprived of our civil rights of access to public services and city-owned infrastructures," the Muslim women said.