How long do have from the time you leave Normandy until you have to be in Geneva? You have options. You can take an Air France flight directly from Caen to Geneva.
You can drive down towards the Loire Valley and then across towards Macon/Cluny and then Geneva. I think it would take me a lot longer than the EDIT 9 hours google maps (7.5h around Paris) says it is because I’d want to stop so much. If you drive all of the way to Geneva confirm that there would be no drop off fee for returning the car to a different country. I seem to remember that Geneva’s airport is close to the French border.
You can take the train all the way from Caen to Geneva but i think it involves going into Paris to change train stations across town.
It kind of depends on how much time you have and cost if that is a consideration. You can purchase less expensive airline and train tickets early rather than last minute. Gas and toll costs can be calculated more accurately on via Michelin. For driving times consider more time than via Michelin states if you want to sightsee along the way.
Good luck with your initial decision.