Being an integrated part of French Republic, Martininque is considered as European as Paris politically, therefore European Union immigration rules apply. In short, EU citizens and citizens of many other industrialized nations can visit Martinique visa-free, others need a Schengen Visa. For more details, see European Union article.
However, if you are on a round the world trip on your own boat, and have an expired Schengen visa while in need of a valid visa for entry into Martinique, it’s reported that the customs officers don’t care much about the situation and let you in – since you are supposed to leave the island in a short time.
From Germany, FRA via Paris: Air France (http://www.airfrance.com/) ~700€ round trip.
From USA, Norwegian Airlines, American Airlines American Eagle is once again offering flights to Martinique, most include a stopover in Puerto Rico. (https://www.aa.com/index.jhtml).
From Canada: Air Canada (http://www.aircanada.com).
From the surrounding islands, you can use these ferry companies:
Express des Iles (http://www.express-des-il...)
Brudey Frères (http://www.brudey-freres.fr)
Cruise ships often visit "in season". Modest-sized ships can dock near downtown, and others moor in the Fort de France harbor, with passengers tendered to docks also close to downtown.