From Europe, Air Caraïbes and Corsair fly year round to the french Caribbean islands with direct flights from Paris Orly airport (ORY). Just like Air France who also operates flights from Roissy Charles de Gaulle (CDG).
From USA and Canada, flights are operated in the winter season. Lookup and compare easily your flights by using a flight comparator like Kiwi with the booking engine just below.
If you live in the provinces or borders of France, Air Caraïbes offers the TGV AIR formula which allows you to book the plane and the train in a single reservation. Guaranteed connection, preferential rate, guaranteed rail station - airport shuttles... An interesting formula, which will also save you parking fees if you plan to go to Orly by car. Note that there is a car park a little outside Orly for long-term parking, at a lower cost.
Here are the cities served by the TGV-Air Caraïbes formula: