From your previous post you said you were planning this trip for April.
I'd not get a car at first. Day trips from Munich are easy with the daily Bayern ticket. Suggestions for day trips: Nuremberg, Rothenburg, Bamberg and others. Come to think of it, Nuremberg might be a better base for these as you can travel very cheaply on the local VGN ticket. You could actually do day trip to Munich from Garmisch.
Hopefully, the border situation at the crossing to Salzburg will be cleared up by then. Rent the car in Salzburg, as it will come with an Austrian vignette. Keep the car in Garmisch and vieit Neuschwanstein in nearby Fuessen. Since Innsbruck is very close to Garmisch, you could hit that city from Garmisch. After leaving Garmisch, you could visit Innsbruck and drop the car there. Then travel by train to Zurich. There is a direct TGV train from Zurich to Paris every 2 hours and the trip takes 4 hours.
After Paris, take the RER train out to CDG airport and rent the car there. Return from Normandy and drop the car at the airport for return flight home.