score:2
On your way to Paris, you don't have to check in or go through security at Atlanta. Your bags will be checked through and it will be just like a domestic connection as far as you're concerned.
On your way home, you will need to go through passport control and customs in Atlanta. You'll go through passport control, pick up your checked bags and take them through customs. As soon as you get through customs, there's a counter where you can drop your bag for it to be taken to Asheville. You'll then need to go through security again (you might have taken guns and knives and liquids and more guns out of your checked bags) but it's a dedicated checkpoint just for connecting passengers and the lines are usually short. Then you're good to go for your flight back to Asheville.