Camping is one of the most popular ways the French themselves holiday, and the country has an extensive network of campsites to match, from large coastal resorts to small rural municipal sites. Most campsites accept dogs as a matter of course rather than as an exception, though — as with hotels — policy, fees and any breed restrictions are set by each site individually rather than by one national camping body.
The near-universal practical rule across sites is that dogs stay on a lead within the site itself, for the same reasons it applies anywhere: shared pitches, children, and other guests' pets in close proximity. Most sites also cap the number of dogs per pitch and expect waste cleaned up immediately at the site's own disposal points, similar to camping etiquette elsewhere in Europe.
Large municipal and rural sites, away from the biggest coastal resorts, tend to be the most relaxed about dogs and the easiest to access directly from surrounding countryside — worth considering if a hiking-focused trip is the main point of your visit rather than a beach holiday, where some sites impose tighter restrictions during peak summer weeks.