Some observations -

You appear to have five segments in Asia (the first one and the last four) - you're only allowed four (only two of which can be stopovers).

Not sure how many of these flights have full F. Most of the AA flights in the US will be 'domestic' F and CDG-JFK is usually a 2-class 767 (no F). Check how many flights you will get 'real' F on before you spend the extra money (unless the CX MPC program makes it worthwhile).

Itinerary is currently 40,590 miles. To maximize miles (if that's a goal) in the U.S., consider Anchorage (ANC) - summer season only, though.

LHR-CDG is a tough one - every time I think about putting this in a trip, it always seems like a lot of effort for such a short distance. You could always go somewhere else in Europe and drop a U.S. leg - using AY or IB can move you round Europe without having to rely on LHR/BA - perhaps LHR-HEL-CDG or LHR-MAD-CDG for a few more miles.

Not sure if MIA/DFW/ORD are in there because they're AA hubs or because they're places you actually want to go?