Each country has its own rules. The relevant laws apply to those countries where you intend on taking on or disembarking passengers. Some of the French islands are part of the EU so you won't have (too many) problems there. What countries are on your list?
Starting on the NW: USVI/USA - no go, see the Jones Act.
BVI - despite being a red-ensign flag state, requirements there can be difficult, but if you jump the licensing hurdles you can pick-up and discharge passengers there
St. Martin - French side is EU, Dutch side is possible to get a license
- Don't know
St. Barths - difficult, plus nobody flies there to start or end a charter
- another ex-British colony with strict rules