I assume you've already made all your travel plans, so not able to change anything at this point.
IMHO, given the destinations you're visiting it would be easier to travel by train and forget the car. The Swiss transportation system is excellent! However, if the car is already booked, I suppose you'll have to continue with that. During your visit to Mürren, you'll need to park the car in Lauterbrunnen or Stechelberg, and take one of the lifts. If I were doing that trip, I'd park in Lauterbrunnen and use the BLM route to reach Mürren. You'll need to specify "BLM" when you buy the tickets. That involves taking the cable car that's right across from the rail station in Lauterbrunnen and then connecting with the small mountain railway at Grütschalp for the final leg to Mürren. It's a very quick and easy trip.
I may have missed when your trip will be taking place? I've not checked to see if any of the lifts will be out of service for maintenance.
I would have probably used the high speed TGV from Zürich to Paris also as it's so quick and easy. I assume you're departing from CDG after that?
The trip from Mürren to Zürich airport is less than 3.5 hours depending on which departure you choose. For example, using an arbitrary date there's a train departing on the BLM route at 07:28, arriving ZRH at 10:44 (time 3H:21M, several changes, price shown tonight at CH$35.80 PP).