I wouldn't suggest North, as that's where we are, so that'd be selfish of me.
If up here I'd suggest Jimmie Davis State park, aka Caney Lake. Shaded sites, nice laundry/bath houses.
Poverty Point Reservoir might be good for fall, but it's a new park, no adult trees yet, except those sites that are backed up to the woodline, so it's HOT in July/August. It has more for the kids....a splash pad, etc. Nice bath houses here too, not sure about laundry.
BOTH sites have fantastic fishing, both sites have marinas, though Poverty Point's marina is more developed...bait store, etc.
Both of these parks have spacious sites.
dcheatwood is in Natchitoches so he may know of some good mid-state locations.