While it’s awe-inspiring to look up at the Eiffel tower, I wouldn’t recommend going up it. It consumes too much time. If you want a nice panorama, go to the steps of the Sacre Coeur on Montmartre instead; it’s free and there’s no wait.
I’d also skip Luxembourg. For a spectacular garden, go to Bagatelle instead; it will be breathtaking in late May.
Notre dame, yes. Try to see the hidden but absolutely spectacular Saint-Chapelle while you’re in the neighborhood. Oh, and go across the river from Notre Dame and visit the tiny and humble St. Jean le Pauvre. It’s pre-gothic, and parts are much older than Notre Dame. Its grounds also have the oldest tree in Paris, propped up to keep it from collapsing.
Pere-Lachaise, definitely.
Invalides only if you’re a military history buff, or a Napoleon enthusiast.
Blvd. St. Germain is interesting more for the people who used to hang out there than for what it is today. If you want to go pay your respects to the ghosts of your favorite authors, go ahead. Otherwise, you’re just paying too much for coffee.
Stroll around the Marais area (4th arrondisement, near Hotel de Ville) to get a feel for what Paris was like before Napoleon had his way with it.
Avoid the Champs-Elysee like the plague. Absolutely nothing of interest there.
Don’t go to Bastille either, because there is no more Bastille. You’ll just find a column and a Metro stop in a sketchy neighborhood.
For pastry, look up Dalloyeau or Lenotre. You can’t go wrong with any of their stuff. For chocolate, make a pilgrimage to the original Maison du Chocolat on rue du Faubourg St. Honore. If you go there, you’re close to a really good cheese shop, Alleosse, on a nice little market street.
Just so you know, you’ll have to go pretty far from Paris to get into decent wine country.