Anyone got recommendations for what to see in Paris?

I used to listen to my then boss going on about how much she loved Paris, and I couldn't see what was so great about it. But my experience of Paris was (with the exception of a course in La Défense) all bar limited to getting between the Eurostar terminus in Gare du Nord and whichever train station I was connecting to for my onward journey; it took a riverboat cruise on the Seine for a friend's wedding reception for me to appreciate there was a beautiful city above ground that I had been repeatedly completely bypassing. So now I'm going with aviva_m for a long weekend; it's my (somewhat delayed) fortieth birthday present from her.

I've actually done Paris as a tourist before, but the last time was twenty-three years ago; I can remember little of it. So I'm intending to skip the few things I remember from then—the Eiffel Tower, the Arc de Triomphe, the Champs Elysées. The question is what else to see. Googling reveals a wealth of Paris tourist sights; the difficulty is narrowing it down. The Louvre is a given, I'll do that on the Friday (and Notre-Dame is ruled out as cohen-unfriendly). And I intend to spend Shabbos afternoon wandering around the Île de la Cité and surrounding area. But what else counts as a must-see; any recommendations?