The short answer is yes, the major tourist sights really are worth seeing. Notre Dame really is the most beautiful thing ever crafted by human hands. I hope you're not bringing any whiny kids with you. If you have an appreciation for medieval history, you can go into Notre Dame with a quiet and meditative air and the pillars themselves will speak to you in the voices of the men who made history, but the illusion is broken if you have any whiny kids along tugging at your shirt and wanting to go back outside for ice cream.
I had the wife with me last time. She did the tour but she too got impatient and went outside for ice cream. I spent an hour alone with the great stone pillars and dreams of the glories of the twelfth century.
St. Paul's is overrated, I think. The best cathedral to see in London is Westminster Cathedral. It's walking distance from Westminster Abbey, which is also worth seeing. But Westminster Cathedral is the real piece of eye-candy. Despite being built in the 19th century, it has a staggering beauty that is rarely seen in buildings that modern. Honestly. If you only have time for one building in London, Westminster Cathedral is it.
If you're into modern, there is literally a shitload of amazing new buildings in London that weren't there last time I was. If you manage to see the new headquarters of Lloyd's before I do, I will be intensely jealous. One of the world's best modern-art collections is in London, too. If you're into modern, go see the Tate, without a doubt.
The Louvre: All the guide books will tell you, you cannot do it justice in a one-day visit. If you try to take in the whole thing in one day, you will be tired and haggard from running around, and you won't really have any new appreciation for any of the pieces. Since you've got only a week for two cities, you can't afford the three days that a real tour of the Louvre takes. You
MUST do your homework before you leave. Choose which pieces you want to see, know what floor they're on, go directly to those sections and resist the many temptations along the way. What do you want to see? The Madonna on the Rocks? Bernini's Hermaphrodite? Vue de Val d'Arco? You have to know what you like, plan it in advance.
You're American, you probably want to see Delacroix's Liberty....

Myself, I'm a big fan of the early Renaissance, but it's not for everybody. I asked my wife, "what do you think is the must-see at the Louvre" and she said with conviction, "the Iranian collection." Truly, being in the presence of the Lamassu is impressive. If you've never seen a full-size Lamassu, you need to go stand beside one just once. The pictures just don't do it justice.
Okay, I don't want to write an encyclopedia, but there's just two off-beat sites that I would really, really recommend. One in London, one in Paris.
In London, go see Battersea Power Station. (That's the one that's on the Pink Floyd Animals cover, surrounded by early copies of your avatar, actually.

) An unintended monument to industry and power, it's both loved and hated. If you've never seen those four giant phallic symbols rising to the heavens, you haven't appreciated London.
In Paris, behind Notre Dame, visit the monument to the Victims of the Holocaust. Again, avoid yakky tour groups or whiny kids. It needs to be contemplated in silence. I won't try to explain what I mean. Just go see it, preferably early in the morning or late in the afternoon when you have the best chance of being able to meditate alone. Truly art in the full sense of the word.
Then go to Montparnasse and buy a T-shirt.
Have fun on your trip!