Well, you’ve already made up your mind, but I’ll throw my two euros in:
I did the same thing last fall, was vacationing in London and figured that I might as well see a little bit of Paris, as long as I was out there. I actually didn’t like it that much, but I blamed that on my being there alone (and Paris is awfully romantic) and that it was towards the end of my trip, so every single inconvenience annoyed me more than it should have. It is without question one of the most beautiful cities in the world, but I think you have to be in the right frame of mind for it. I just kept thinking how excessive it is.
If it’s a six-week trip, I’d recommend at least three days in Paris. I spent two days and just saw the highlights with no downtime, and it all felt pretty rushed. You will not be able to see all of the Louvre, so don’t even try. I was there for about four hours and only saw part of one wing, and only that much by walking quickly. Just choose the big things you want to see there and hit those and the surrounding area. (For me, I just wanted to see The Raft of the Medusa, and just because it was on the cover of a Pogues album).
I recommend seeing the Sacre Coeur, in Montmarte. It’s far from being an obscure tourist attraction, but I’d never heard of it before. It’s a beautiful building, and is high enough to give you a nice view of the entire city. And the other standard attractions – Notre Dame, the Opera House, the Eiffel Tower (at night), the Pompidou Centre – are crowded with tourists, of course, but are still very impressive sights.
If I can recommend a travel guide, I’d get The Eyewitness Guide by Dorling Kindersley. It’s not the deepest you’ll find, but it’s fantastic for quick, shallow trips.
There are several open-air tour buses that go through the city, and as touristy as they sound, they’re great for just checking stuff off your list, and your ticket is good for the whole day (or two days), so you can stay at a place as long as you want. The lines stop at all of the major tourist attractions.
Getting there, I used the Eurostar from Waterloo to Gare du Nord like everyone else. It’s kind of expensive, but it’s extremely convenient and painless.
As for the language: I took four years of French in high school and college, which means that I can’t speak or understand French. I could make simple sentences in my head as I walked along (“Ca femme porte un petite chien”), but couldn’t speak to anyone in anything other than English. I didn’t have any problems at all, just extremely minor inconveniences. Of course, I did stay in the touristy areas and didn’t try to do much socializing. As Zebra mentioned, say bonjour to start with, to show respect for the language and to make it clear that you’re not French.
In my case, I started out by spending a couple of days in Disneyland Paris, both because of my bizarre Disney fixation and because I thought that as an Ugly American, I could use it to slowly acclimate myself to France instead of just diving headfirst right into the middle of Paris. This was a bad idea all around. The park just isn’t that impressive, even if you like Disney, and the people were actually more hostile and less helpful than in Paris itself.