No there is no park at all, it’s almost all commercialize. You can walk around the outskirts of the Carter House, and a few other areas, but if you want tours of the Carter House grounds you got to pay, If you want to have a tour of the Carnton House about half a mile away you got to pay, but some of the grounds around the Carnton House grounds, or to better say it the property next to it has a walking tour you can walk that has several plaques you can read. A lot of houses and businesses around where they fought.
I went earlier this year. Both tours were interesting to me, though I’ve never had much intertest in specific battles. I’m ignorant, so all of the info was new.