There are already a couple of airlines who do this quite well in Central America. TACA and COPA (two very well run airlines imho) run their respective hubs to connect North, Central and South America.

Also, although the overseas departments are part of the EU, sometimes bilaterals have special provisions (restrictions) for services there - eg the original US-France bilateral had those.

However, this open skies agreement of course also opens the way to US carriers to provide beyond services out of the French overseas departments. Seems much more likely to me than European carriers setting up hubs in the west (except for the IB hub in MIA which was closed down after the more onerous US immigration restrictions were imposed, in effect killing of the possibility of especially Latin Americans to travel with a visa through MIA)