The victim, aged 46, was killed on Saturday at the La Mama beach on a lake in the Lyon suburb of Miribel, regional prosecutors said.
The 75-year-old is suspected of shooting the victim multiple times in the bushes nearby following a dispute that arose after the younger man allegedly exposed himself in front of a woman, they added.
The regional daily Le Progres said that the suspect is a member of a shooting club and legally possesses a calibre 22 rifle. The victim was known to the police, it said.
The Le Parisien daily added that according to its information the victim had been a cause of trouble on the beach all Saturday morning with tensions rising to a peak when he began to masturbate in front of a woman.
An altercation ensued at which point the septuagenarian reached for his gun.
Le Progres said that at the peak of the summer season the beach — well known to Lyon’s inhabitants — was operating as normal on Sunday.
Participants in the World Naked Bike Ride France arrived even as police carried out investigations and images showed naked bathers enjoying the hot weather.