I don't think there are many campgrounds on the Atlantic in Florida. There's an Outdoor Resorts in Melbourne Beach (very nice but sites are pretty small so over 40' probably doesn't fit) and North Beach Campground around St Augustine Beach (not as nice as Outdoor Resorts but decent, older campground with much bigger sites) that are on the other side of HWY1 but you can easily walk to the beach. The ocean is pretty rough at both so may not be suitable for kids or seniors. There's actually another one near St Augustine where the sites back to the retaining wall to the beach but I forget the name.
There's also Fernandina State Park in Florida near the Georgia boarder. We've been but I don't remember going to the beach much but it might be because it was too cold when we went. There's also Jekyll Island State Park in Georgia which I've heard is very nice but I've never been.