FM 747, north of US 84, gets little traffic and offers roadside birding.  The area south of US 84 has unpaved roads entering the forest to look for the Red-cockaded Woodpecker.  Most passenger cars should have no problems here.

Eight species of woodpeckers, including Red-cockaded. Also breeding warblers: Prairie, Hooded, Kentucky, Swainson’s, Black-and-white, pine, Yellow-throated.

From Texas A&M Forest Service:

Like other Texas state forests, the Fairchild is a working, demonstration forest and has served as a site for numerous silvicultural and research studies: harvest cutting, farm forestry, timber stand improvement, reforestation, tree growth, prescribed burning and seed production. The forest also hosts a small population of the federally-listed endangered species, red-cockaded woodpecker. Today, forest management activities focus on habitat protection for this important species of the southern yellow pine ecosystem.