I'm assuming you will fly AA from MIA to CDG? Are your trips in economy class?
IIRC, the last time I flew FinnAir long haul in economy, they did not have personal in flight entertainment and the food was mediocre. I can live with ok food, but I really hate not having AVOD on long flights.
If this is your first time traveling abroad, you will get pretty tired with this itinerary. If the price differential for flying MIA-JFK/ORD/SFO/LAX-HKG is not too high, I would strongly recommend you do that.