I am traveling to France. Booked trip through Delta. First leg is from home airport US, to JFK on Delta, second then is to France via Air France under Delta. So, when I arrive at JFK, will I have to retrieve and recheck my bags when I get to the international terminal or do they check it through to my final destination...and then coming home France to Detroit, Detroit to home airport. Thanks.
Outbound, you'll pick up your bags in Paris (or wherever you're flying there). You will not pick them up in New York City.
Inbound, you'll clear US customs and immigration in New York, so you'll likely have to pick up your bags, clear customs, and then recheck them for your flight home. (Some airports now only make you get your bags if customs officials want to inspect them, e.g. Calgary.)