Is that 4 full days in Paris after your day of arrival? The first day is usually a bit of a blur.
You can wander over to the cathedral of Notre Dame and view whatever is going on, from a suitable distance, but only from the outside due the fire some time ago.
The Eiffel Tower is another story. Seeing it from the outside is the impressive bit, in my opinion best from Trocadero (but watch out for the junk sellers, by the dozen pre-covid). Do you want to also go up? Stairs or elevators? In the before-times there were long queues and tickets in advance were not always easy to come by. Do you want to have a meal at the top?
4 days can pass very quickly, perhaps too quickly to consider a day trip out of town, and definitely the best way to visit Normandy, if you mean the area of the D-Day invasion, is to be staying there and then taking an organized tour. If you are considering a tour from Paris there are some available by some of the best guides. You can take a very early morning train to Bayeux where they will collect you and show you some areas in a short tour and then put you back on a train which will get you back into Paris quite late. Not the best way to do it, and by no means comprehensive, but perhaps better than nothing for you. There are also more plebeian main stream bus tours from Paris to some of the D-Day beaches and catching a stop at Giverny on the way back. In my opinion that is far too much to try to cram in.
If heading to Normandy in June be sure to be aware of the dates. The anniversary times around the 6th will be very very busy.