Martinique is just like any other place. It is within the EU and so you will most likely follow the leads for buying
an EU boat. Unless she is flagged elsewhere.
I think you are after a cat we anchored next too most of last winter.
How I bought our boat I just flew to her, had a good look and a long sit down with her owner. Then I paid the money
and he handed over the keys.
Ask your registrar what it takes to register her in your country. Most countries require deregistration documents along with some form of "bill of sale" and relevant tax papers.
Nice place to buy a boat.