Louisiana has a lot of national forest land. Kisatchie National Forest info can be found at Kisatchie National Forest Recreation Opportunities
The Caney District is north of I-20 and the Winn District is along US-84 which is south of I-20. Corney Lake in the Caney District might make a good stop from I-20.
Louisiana has at least two state parks off of 20 and there is the Lincoln Parish park that Rich Luhr described in Ruston.