I totally agree with Threadwear.
Power through to Bayeux, see the Tapestry (which will be restored and unavailable starting in September 2025 for 18 months) go on at least a half tour of Normandy, enjoy the lovely town and the wonderful restaurants. You will get a different flavor of France and a meaningful historical experience in Normandy. I would highly recommend doing a tour which has you at the cemetery when they lower the flag and play Taps. If you don't get tears in your eyes during that, something is wrong with you. Then the tour can drop you off at the train. If you do rent a car, don't do it the first day when you are tired, still take the train out, get the car the next day, but then you can return it in Paris and you can stop and see Giverny on the way in, which is what we did.
We stayed at Le Petit Matin in Bayeux which we highly recommend and Le Clement Hotel in the 6th in Paris. Le Clement sells out quickly because it is reasonable and extremely well situated, but I would look in that area if it is unavailable. Is 4 days enough in Paris? Of, course not, but it is enough time to give you a nice taste. Paris is not so huge that you couldn't see a lot of a first time wish list. We have been there 6 times and our list keeps getter longer. Leisurely enjoy what you can and there is always next time! Enjoy!