In reverse order:
-The only thing to be upset about is your luggage... that sucks. Other than that, the rest of your story is on par with all other travel "horror" stories of the past couple of weeks.

-As long as CDG is open, then it's AA's obligation to get you there. Imagine the posts saying "I was on AA to CDG and they landed in MXP instead. There aren't any flights to CDG and now I'm stuck without a hotel because AA says it's weather."

And no, AA did not break FAA rules. Pilot logs are tightly regulated and the fines are REALLY bad, including possible action against the pilots including them potentially losing their licenses.