My girlfriend and I went to Paris at the end of June, 2002. Here is a very small subset of my pictures:
http://www.abigguy.com/pics/france/
You've already gotten quite a few great tips, but I'll add my twelve cents:
We arrived from London via the Eurostar, as you will. Gare du Nord has just about everything you need: an ATM machine, an information booth, and a ticket booth (downstairs) selling Metro and Museum passes. If you're going to be there for a while and plan on taking the Metro a lot (I'd recommend it), you can get an Orange Card, which will get you on all public transit (bus, metro, RER) within the city center for a week. There's a similar 'tourist card', but it's significantly more expensive for less value and fewer days. For the orange card, you'll need to use a photo booth (there's one right near the ticket window) to get a passport-sized photo. The photo gets taped to the front of the card, so that people can't share cards. The photos were 8 euros, so you may want to use your 717 and a photo printer to make your own before you go.
For getting around the city, take a book (we liked the Eyewitness books) to plan your day and a good map (Streetwise Paris is a WONDERFUL fold-up map of the city center and the Metro system) to get around. To navigate the Metro, see where you are, see where the nearest Metro station is, and figure out which lines stop there. Figure out where you want to go, and find the nearest stop (and the Metro line). Then flip the map over (if you've got Streetwise Paris) and look for a station that connects the two lines. Get on the first line by looking at the final destination in the direction you wish to go, get off at the transfer stop, and get on the new line in the right direction. We mostly used the Metro, but also took the RER a few times...Line C was pretty useful.
I didn't feel unsafe anywhere, though I decided I wouldn't want to hang around in Montmartre or near the Moulin Rouge after dark. We stayed at the Hotel d'Albe, in the Latin Quarter. The rooms are small (like most European hotel rooms), but we had our own bathroom and a great view of the little pedestrian-only streets in the Latin Quarter. There were also about 100 restaurants (literally) within a two-block radius, and Notre Dame was two blocks away. Many other sites (the Louvre, etc) were a healthy walk away, but the Metro was so close that we ended up taking it everywhere. After staying a week and still not seeing everything (but seeing quite a bit), here is a list of nice sights, basically in the order that we saw them:
Notre Dame- I'd especially recommend climbing to the bell tower...long line, but worth it
St. Chapelle- it was small and not quite as impressive as I expected, but great if you like stained glass
Seine Cruise- pick it up near the Pont Neuf...try it early, as it'll give you a good sense of the Paris layout
Eiffel Tower- duh.
Sacre Coeur- beautiful white marble Byzantine church at the top of a great hill (see my pictures)
Moulin Rouge- not that impressive, but well-know
Pompidou Center- monstrous modern art building...interesting architecture and cool fountain
Arc de Triomphe- pretty impressive...definitely climb to the top
Champs Elysees- not much was going on while we were there...still a must-see
Petit Palais/Grand Palais- closed when we were there, but they looked neat from the outside
Place de la Concorde- a large square with fountains and an obelisk
Opera House- the Phantom of the Opera is there
Place des Vosges- neat little square w/ cool architecture and a nice atmosphere...maybe not during the winter
Pantheon- impressive building, but they only let you climb the dome at certain times
Luxembourg Gardens- GORGEOUS during the summer...can't say for winter
Hotel des Invalides- Napoleon's tomb....big for a little guy
Museums- I'll reserve a paragraph for them
You can get a museum card at the same ticket window in Gare Du Nord. They have 1-day and 3-day....I'd definitely recommend the 3-day. It'll get you in just about every museum free of charge, as well as some other must-see places (like climbing Notre Dame or the Arc de Triomphe). Most museums, it also gets you to the front of the line. We spent a day in the Louvre, and I was most impressed by the statues and the architecture of the building itself. A lot of the other art is nice, but didn't really appeal to me. The Musee d'Orsay is wonderful, and definitely a must-see. This was also my girlfriend's favorite. The Rodin Museum is great if you're a fan...I especially liked his early work. The sewer museum is one to stay away from...I'm not sure what I was thinking, but it smells pretty much just like a sewer.
We took a bus tour that visited Giverny and Versailles. It was arranged by Paris Vision (the tour company...you can find them online), and it was a great trip. They pick you up at their offices (near the Tuileries/Louvre) and take you on a nice double-decker bus to Monet's house. Nice, English-speaking tour guides give you a nice introduction, then let you walk around and take pictures of the flowers. They take you to a beautiful restaurant for some great food for lunch, then onward to Versailles. You get time to walk around by yourself, then a guided tour of the interior. I'd definitely recommend taking one of these bus tours.
After Paris, we went to Tours for two days, to see the chateaus, and Dijon for two days, to see the mustard (and go on a day trip to Switzerland). If you leave Paris, I'd recommend the chateau tours. The city of Tours is less than idyllic (picture a humid little river town during the summer...the mosquitoes were nasty), but the chateaus are gorgeous, and make great photography subjects.
As a disclaimer, the weather was perfect when we were there....your mileage may vary. Feel free to email if you have more questions (or want more pictures of anything in particular).
-Jaime