I'm no lawyer, but will speculate US courts don't have jurisdiction over an EU regulation.
Regardless, my understanding of the EU regulations is that AA would not be covered on flights from the USA to the EU as they are not an EU based carrier. However, the flights would be covered if the AA flight departed the EU to the US. In that case, if unsuccessful via normal routes, there are quite a few companies in the EU that will manage your claim for you for a percentage of the amount - even going to court on your behalf if necessary. There are also means to file a government complaint in EU countries.