Get a French bank account, get a French Flying Blue Amex and all purchases count toward status miles, which get you status with Skyteam. (Not a realistic suggestion, but I did want to point out that the Flying Blue Amex is one of the few cards I'm aware of where purchases get you status miles.)

How close do you live to Canada? You could get a CIBC Aeroplan card with Maple Leaf Club privileges, and this would give you business class check-in and lounge access for Air Canada (which has a good international network), with some check-in and lounge access benefits for code shares with United up to Canada. A silly suggestion if you live in Miami, but not out of the question if Toronto, Vancouver or Montreal would be decent hubs for your international travel.