Are the French really rude?

Tough question.  I would say that Parisians are definitely the most snobby/over it French people I have met, but that's because they deal more with American and Asian tourists than actual French people.

That being said, the French have a really strong culture where everyone knows the rules (meaning mostly propriety, decency and not walking on the grass).  If a foreigner such as myself breaks one of these rules, it is fair game for any French person to correct (or rather scold) me.  Adults correct other people's children (and the parents don't mind), and the French must correct foreigners constantly.  And where is the largest concentration of foreigners?  Paris - by a mile.  Americans come to Paris and act like Americans, meaning they're breaking about 100 cultural rules just by being themselves, so there is constantly a conflict that Americans don't understand.  Also, I'm sure it's annoying to be overrun by tourists, being that France is the number one tourist destination in the world.  I believe that is why the French stereotype of rudeness is alive and well.  So is it true?  Well yes.  But they're just following their cultural norms.  Is it still unpleasant to interact with many of them?  Well yes.

In Lyon and other parts of France, the French are so much nicer and accepting of foreigners.  I cannot think of one conflict that we had with French people in Lyon (except for people correcting my grammar, which isn't a big deal).  In Paris, there were many conflicts.  I was surprised that I was corrected (or scolded) so often because I speak the language and I lived in Paris for a few months, so surely I understood the culture.  During our last week in Paris we learned the hard way that one must always follow "the system" exactly, even if we think it is inefficient.  Should people still go to Paris?  Absolutely, just try not to go during the summer.

We are glad to be back the US, and after all of our experiences, we are still very fond of France and want to return.