Paris is like any other big European city: very busy around the main attractions. I find that too often tourists who don't deal with crowds well didn't like the cities they visited because they didn't spend enough time in them, and spent what time they did have running from one of the Top 10's to another! No wonder they didn't have a good time.
I can manage crowds pretty well but we do better with longer stays so we can balance visits to the "tourist magnets" with time away from them. Paris is pretty spread out so finding breathing room isn't difficult to do. For instance? I believe I read on one of your previous posts that you're into cemeteries? Paris' biggies are great places to wander without being overrun. I spent 5 hours in Père-Lachaise, and another 3 or so in Montmartre one morning. We saw very few others, and Père Lachaise is so huge that it can handle a LOT of visitors without bumping a single elbow. I hope to get to Cimetière du Montparnasse next time.
A couple of other suggestions for finding space:
Parks: Paris' green spaces are good spots to lose the mobs. We enjoyed, say, Jardin du Luxembourg very much. While not deserted by any means, neither was it overrun.
Take advantage of any late openings at the "tourist magnets". The Louvre, for instance, is open until 9:45 PM on Wed. and Friday so it's a good opportunity to browse the works while many other tourists are at dinner. The d'Orsay is open until 9:45 on Thursdays, and the Arc de Triomphe is open quite late every evening (hours vary).
Look at visiting some interesting places that a lot of tourists overlook? We thought Musee Cluny/Moyen Age was wonderful, and it wasn't what I'd call "busy" at all. Same for the Pantheon and a couple of others.
Consider skipping some places that will be busy ALL the time: we bizbagged a trip up Eiffel and were never sorry. There are other good vantage spots in Paris. Besides, when you're ON it, you can't SEE it! The Trocadero is a great spot for viewing the Tower at night. Yes, it's a busy place but it's free, and you can stay as long or as little as you wish to.
Sightsee when others aren't: early mornings are great times for hitting some of the more congested areas without being run all over. We also tend to eat very early and have walkabouts when many are occupied with dinner.
Lastly, embrace the crowds while not being in the thick of them. Pulling up a chair at a sidewalk cafe and just doing some people watching is great fun!!! :O)
We spent a week in both London (my second time) and Paris and loved both for the riches of history, architecture and art. Sirens? Yes, you will hear plenty in Paris but they're nothing to worry about: just a factor in any big city. :O)