I'm sure Capttim's heart is in the right place--even if his fingers aren't.
However, to truly optimize your visit, I suggest buying a guidebook and determining your own personal, subjective set of "must-see" sights. There's certainly some overlap between some of my favorites things to do and see in Paris and Capttim's list--but it's far from a perfect match. Yours wouldn't perfectly align with either list--or perhaps anyone else's list.
I have yet to buy a guidebook that didn't pay for itself in terms of the time, money and effort it saved me. And for me, there's always been a big enough difference between the good/great time I would have had in a destination without a guidebook, and the optimal time the details in a guidebook helped me to craft to my specific, oddball tastes.
I'd also note that you're under no obligation to visit any of the most famous sights if they hold little appeal for you even if other people expect any visit to Paris to include them. Especially if they involve waiting in long lines and/or running a gauntlet of would-be pickpockets.
My own list of favourites would include The Cluny, Musee D'Orsay, The Rodin Museum, The Musee Carnivalet (for a quick, painless overview of Parisian history), maybe Pere Lachaise cemetery. And whatever it's drawbacks, I wouldn't outright dismiss The Louvre. Then again, I'm an art maven and if you're not, you might give it a miss.
Finally, if you're going out of your way and spending all this extra time and money to visit Paris, I'm not sure a day trip out of Paris is the best use of your time. Even with 6 days, there's plenty in town to keep you occupied. Especially if want to spend a morning or two just wandering around various neighborhoods (the Marias, Latin Quarter, etc).