It seems like you have an itinerary planned, but it seems odd to drive directly from Bayeux to Amboise. They are not very close to each other, and there are many potential stops in between. Are you interested in Fontevraud Abbey? Dinan? It's pointless for me to say that MSM is "better" than Bayeux, but the really important difference is that MSM is farther from Paris and MUCH harder to get to without a car. Your note about Caen suggests that you don't plan to spend vast amounts of time on the D-Day sights/sites.
I don't know if it still works, but old Rick editions had a scheme to put your luggage in the trunk of your rental car in Rouen, and LEAVE IT in a relatively safe rental-car only garage after you rented it, to walk around Rouen. Haven't done this. My last few car rentals have been pickups in the open air.
Note that many car rentals close for a two-hour lunch in France. Have you considered doing the trip in the opposite direction, taking the TGV to St. Pierre des Corps and doing the Loire first? Not saying which is better for you. Is it a one way car rental, and was there much of a fee for the drop-off? It's great to get over the jet lag, but you could argue (any actual experience?) that half-hour drive is doable on arrival day, and that your departure schedule (from Paris home???) works better with the 4 days at the end. That mainly depends on the flight time, but also on hotel location the night before returning home.
