Paris is just so huge that it's hard to answer without more details about what you like.

General tips:
-echo the previous poster on language: basic French helps a lot;
-I was there over East two years ago and had brilliant weather, but it can be cold too. Check the day before leaving and play accordingly;
-The Louvre requires at least one full day to enjoy and probably more than one if you want to do more than run through and glance at the Mona Lisa;
-Sacre Coeur is spectacular;
-I'm not a Notre Dame de Paris fan: Strasbourg, Cologne and Milan are better as far as cathedrals go. It's worth a look, but not a lot of time in my book;
-If you poke around just south and east of the Opera, you can find good hotels very close to the tourist center of gravity at remarkably low prices. It's pretty quiet there, but the convenience is great;
-Good restaurants are everywhere (it is France...), I won't even bother with recommendations;
-If the weather is nice, you could spend a relaxing day just hanging out in the Luxembourg Gardens. I love to go there to watch the old men playing chess over on the West side of the park.
-Hit Montmartre in the morning, fairly early. It's got a great feel to it. Just buy some fresh fruit from a vendor and stroll.

Yeah, buy a couple of guidebooks and peruse carefully. There's no end to what you could do in 10 days.

Now I'm jealous, maybe I need to go back...