No, you can't use a Schengen visa to go to Martinique. You need to get a separate visa from French embassies or consulates to go to Martinique.

People who don't need a visa can stay in Martinique for up to 90 days in a 6-month period.

No, Martinique is not part of the Schengen Area. However, Schengen countries and their citizens do have some rules that are easier to follow. EU and Schengen country citizens can go to Martinique without a passport for an unlimited amount of time with their National Identity Card.