Is this car idea crazy?

If all you intend to do is 'drive by' then it is doable.

If your plan is to actually visit the sites and attractions, then your plan could probably fairly be described , as you say, 'crazy'.

There is no 'leisure time' in the plan that I can see

my $0.02

It’s realistically about 15-16 hours driving. Doable? Yes. Pleasurable? Not in my book.

Versailles is much quicker by public transport. Hiring a car in the centre of Paris isn’t a good idea if you don’t know your way round.

I would pick either the Normandy beaches OR the Loire as both need 2 days minimum to do them justice.

In terms of just distance, this is akin to asking if it would be possible to rent a car and do Boston and Salem, Albany, and New York City, all in 4 days. Doable in terms of driving? Sure. Worth it? Not in my book.

To do justice to the Normandy beaches, stay for two nights to allow a full day on an organized tour. The story matters as much or more as seeing what remains on the ground from 75 years ago.

As much as it seems achievable, you might not be able to optimally experience these places within that timeframe. You might want to review your options.

Which place is most important to you? I think you need to drop one of those locations. Either do Versailles and then the Normandy beaches, or do Versailles and then the Loire Valley. You'll still be a bit rushed with only 4 days but it's much more doable. There's too much distance for all of them in 4 days.

I agree with the other posters. This would allow no time for actually experiencing even at a minimum level what these sites have to offer.

I agree with the other posters to limit yourself to Versailles and Normandy or Versailles and the Loire Valley. If you choose the latter definitely rent a car, since having a car in the Loire Valley is very beneficial. However, if you prefer Versailles and Normandy I would use trains. The train to Versailles from Paris is very easy and you can purchase your ticket at the Metro station. The train ride to Bayeux takes about two hours. As a previous poster stated spend two nights in Bayeux so that you can take one of the full day tours of the Normandy beaches and battlefields. There are several good companies that have small group mini-van type tours with a knowledgeable guide that brings the history to life. We used Overlords last October and the D-Day tour was a highlight of our trip to France.

Thank you all so much, I appreciate it!!!