Take this little sandy alcove, for example. I noticed it while biking up a hill near Six-Fours-les-Plages. Out of sight from the average beach-goer, it would make for a quiet, stress-free day in the sun. Sure, I wouldn't try to hike down to it in my flip-flops, but with some good shoes and a light load getting there could be half the fun. There are of course options that require a little less mountaineering to find. It suffices simply to explore the spaces between the public beaches - areas along the cliffs and rocky out-croppings are great - in order to find more off the beaten path locations.
Of course, the public beaches do have their benefits. They sometimes come with amenities such as restrooms and showers for rinsing off the sand and salt. Their lifeguards can give extra assurance to parents, and when it gets too hot you can grab an ice cream cone at a nearby stand. There's also the issue of ease. Finding a public beach is a lot easier than searching for a quieter one. But I'm convinced it's well worth the effort to do a little hunting before choosing your spot. While lounging in the sand with only the sound of the rolling surf as your company, you'll be happy you're not fighting the crowds for an extra inch of beach front.