Consider Chattahoochee Bend State Park, west of Newnan. It's about 30 miles from Peachtree City. It's a relatively new SP and I have not been there yet. But it's on the Chattahoochee River and they have 40-ft pull-through sites available. You can reserve for your length, but you cannot reserve a particular site.
Honestly, there is just not much along that I-85 corridor, except at West Point Lake, which is probably going to be too far for you. It's right close to the Alabama line. Indian Springs SP and High Falls SP are off of I-75, so it's a good hour or more from Peachtree City.