Notre Dame and Chapelle are a 5 minute walk apart, and they don’t take all that long to see unless you want to wait in que to go to the top of Notre Dame, something I never did whilst living in Paris, so I can’t say if it’s worth it or not.
Sacre Coeur is woth the trip up the hill. You can see the inside of the church in 20 minutes but the view from the front over the city is great. Lots of people up there, a good place to people watch. The are lots of cafes up there , some a bit touristy, but I never minded. Within walking distance is a GREAT place to eat. It’s called Moulan something or rather and has an old wooden windmill on top. From there, you can walk down the hill to Pigalle (or Pig Alley as US GI’s used to say) and see the Moulan Rouge and all the Japanese tourists going in. (My French friend theorizes that no actual French person has been inside in decades) Pigalle is kind of seedy but good for a lark. Not sure if it’s your thing or not, but DO NOT go in any of the “strip clubs” in Pigalle. They are seedy whore houses and clip joints, some things haven’t changed since '45.
If you are into militarty history and armour and the like, go to the hotel invalides, the former old soldiers home converted into a museum. I have never seen so many arms and armor before. The stuff they have in storage on shelves (there are windows to see in one of the store rooms) would be the centerpieces of a lot of collections in the US. There is a really interesting chapel on site that displays flags captured in French military victories from various eras. I believe these these used to be in Notre Dame at one time. Also on site is Napolean’s tomb, which is quite striking. Biggest freakin coffin I ever did see, and for a little guy too.
Luxumborgh gardens are nifty in the summer, I don’t think I ever went in the winter so not sure what to expect. The senate is there, the building headquartered the Luftwaffe during the ocupation. I don’t think you can go in as a Pierre Everyman.
I like to stroll from the Louvre past Concorde down to the Arch de Triumph (the big one, not the first one you pass) You can take cool photos of Triumph from Concorde down the Champs with La Defanse (the modern office building with a big 'ole hole in it in the distance) You can take in the shops on the Champs on this walk, if that’s your bag. Beretta has a beutiful store off the Champs next to the Kazak embasy if you like old school hunting stuff or just want to see a 77,000 Euro shotgun (it’s in the back)
Don’t be afraid to ride the metro, it’s pretty easy to figure out. There are easy to use machines that give you instructions in English that you pay with Euro coins. If you are there on a weekend, you can get a whole day pass for less than 2 Euros, it’s called a ticket de Junne and I THINK you have to get it from the cashier, not the machine, but it’s a real bargin. (You just want zone 1 unless you are going to Versilles)
You probably won’t be there long enough to get homesick, but if you’re interested, I know about every English speaking bar in town. Let me know if you’d like some help on the nightlife front.
Probably obvious, but it gets damn cold in the winter. If you are going in the spring, remember only tourists, small children, and Germans wear shorts.
Don’t be fooled by the Eastern European girls staking out tourist spots. They will ask you if you speak English and then hand you a paper detailing a sob story about needing money to get back to Bosnia or something. I’d see the same three or four girls all over town for 9 months. (My mother was horrified I’d tell the girls I didn’t speak English when she visited)
Hope you like second hand smoke, and that you have a great trip.