France can be divided into Metropolitan France (the main hexagon of France, along with Corsica), Départements d'outre-mer (including Martinique, Guyana, and others), and Collectivités d'outre-mer (such as Saint Martin). In terms of US geography, the rough equivalents are the continental US, Alaska and Hawaii, and unincorporated territories of the US (like Puerto Rico). If you don't understand the latter term, think of it as a fancy term for colony.

Well, sort of. Looking briefly at many maps of France (in French), the inclusion of the DOMs are relatively rare, in contrast to the inclusion of Alaska and Hawaii on most US maps. Corsica is about as prevalent as Alaska and Hawaii (probably more so), while Guyana and the other DOMs are about as prevalent as Puerto Rico.

French Guiana is the departement (and region) of France that is on the South American continent. It is as much a part of France as e.g. Alaska is of the USA.