I've had the wonderful luck of having visited Paris many times, with more times to come in the future, I'm sure! With each visit, I not only crossed off the big things to see in Paris, but also discovered more out of the way, or less known places to go and see.
First, let me clarify by the "big" things one must see during their first visit or two to Paris:
La Tour Eiffel, the Louvre, Sacre Coeur on Montmartre, Notre Dame de Paris, The Latin Quarter, Pont Alexandre III, etc. I'll never say to not bother with these places, they are all spectacular in their own way, and all still very much of Paris. If you are looking for things on the path slightly less taken, or very much local and authentic, here are 8 other places you could add to your list.