Unless there is something in Chattanooga you want to see, I would suggest staying on I-40 to NC and take Hwy 23 (Exit 27) which will be nice dual lane road to Franklin. Hwy 64 from Chattanooga is a lot of single lane curvy road to just outside of Franklin. Doable, but not enjoyable with your rig. Adds 50 miles to the trip but think it's worth it. This is based on local knowledge from having land near Sylva, NC and wheeling for years in Tellico Plains.
If you want to stop for a night before you get off the interstate, there is a nice campground a couple miles before you exit the interstate at Hwy 276 called
Creekwood Farm.