Upvote:3
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.)