I would take a train out of Paris and rent your car when you get to the Champage region.
You should plan each day’s drive and driving time based on the roads you’ll be taking. It’s not like the US where you can assume 300 miles in 5 or so hours. On highways, sure. But once you get off the hughways, many of the roads go from town to town, slowing down as you approach and leave each one. Toss in getting behind a line of cars and trucks and it can be a long afternoon.
A decent planning tool is the Michelin website.