Depends how fast you go when towing, but we managed Normandy in just over four hours from Calais. We can recommend the muncipal site in Courseulles sur Mer link to reviews here. Alternatively the Champagne region is good (Rheims, Epernay etc) Le Croix de Vieux Pont here is not a bad site, but quite pricey
Hope you have a good time
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Leebee, if you choose a place or an area you want to visit it might be possible to suggest sites, but 4 hours driving could take you almost anywhere. Hope your trip goes well.
Like others, it's difficult to suggest a site - there must be thousands within four hours of the tunnel. What do you like doing? What sort of site? Some people want plenty of nightlife, and an all-singing campsite, others want quiet and restful, with five pitches in an orchard and some want in between.
It would help to know. The only thing I would say is that in mid-September there is absolutely no need to book and the best way of all is probably to highlight a few areas you'd like to visit and then 'on the day' just head in the direction of the best weather forecast.
Don't forget to leave a review of the French and other European campsites you have visited!