My way of touring a city begins with hotel selection. In Paris, I choose to stay in the 6th arrondissement in St. Germain de Pres. We are returning there on May 2, prior to our Provence sailing on May 9. If you choose to walk, you'll find yourself immersed in history here. The Seine is a hop skip and a jump away. Next to the church is the metro station. Taxis abound.
My suggestion is to look at a map and orient yourself to where and what you would like to see and then buy advance/skip the line tickets. Musee L'Orangerie is small and wonderful, lunch on the Eiffel is fun, the Catacombs are worth a visit. There is so much to see. Enjoy!