Paris is class, how long you going for? You'll deffo have to schedule in a second visit.
Budget for public transport, you can walk it all but I wouldn't recommend it, walking through the day is fine but it's when you wanna get home is the bastard. An entire day could be Arc de Triomphe, walk to the Eiffel Tower go up, come down, walk down the Champ de Mars and have a butchers at the Musee de l'Armee then walk from there to the River Seine. Pick some lunch up at a boat restaurant on the river, head over to the Place De La Concord and up the Champs Elysees.
Other than the obvious like Notre Dame and the Louvre (which I'd recommend doing together due to proximity), Le Jardin Du Luxembourg is probably the best park you'll ever go to and Montmatre has to be given a full evening, good food, artsy corner of the city and a fantastic view and if you can go in the Sacre -Coeur even better.
Paris is one of my favourite cities.