General infos :
-Money change won't be a problem since you will do Italy before France. Euro zone.
-SNCF trains perfectly accept luggage, no worries ! There are spaces to store it in each wagons. There is only few restrictions on the following lines = for Thalys lines and for Ouigo tickets, where you will need to pay supplement for more baggage than what is allowed. So as long you have money = no luggage problem.
Paris infos :
-It is better to use the subway than buses (RATP lines), and usually you will travel between zones 1,2 and 3.Here a link for more infos
-4 to 5 days is enought to enjoy Paris.
-Almost all big touristic places are accessible by walk.
Places to visit :
-Eiffel Tower by Trocadero place the view is fine. If you plan on entering the Eiffel Tower, do reservation and if possible avoid 10 am-5pm time slot.
-Cité Island with Notre Dame (hmm...), Sainte Chapelle, and many more !
-Starting from the Triumph Arc, going down the Champs-Élysées avenue to end up to Concorde Place. From here you can access two others sites (Tuileries garden+Louvres, or Opera of Paris).
-Latin Quartier in 5th arrondissement, with the Pantheon, Sorbonne, Luxembourg garden, Cluny museum (Middle age museum), Lutece therms, Mouffetard street, la Huchette street...
A link with a detail of each places to visit by arrondissements, it can be helpful because indeed Paris is too big to be resumed in few lines. I personally enjoy mostly Opera quartier, 13th, 16th, and 17th arrondissements for example, but that my personal tastes.
Where to eat and drink :
Usually you will have enough choices to find on your visit a good place to eat and drink, sadly i won't be of any help for this part. But usually TripAdvisor rating and comments are pretty spot on.
After Paris, depending on your ending town, in which town will you end your trip ?