French Guiana is an overseas department of the French Republic. As such, the French Guiana national football team is not a member of FIFA. The citizens of French Guiana are citizens of France so are eligible for the France national football team. An example of this is Florent Malouda.
The Guiana national football team, although not a member of FIFA, is a member of the Confederation of North, Central American and Caribbean Association Football. As such the team is eligible for tournaments such as the Gold Cup. There are some restrictions placed on overseas territories like French Guiana in these other tournaments. For the Gold Cup players for the French Guiana national football team are only eligible if they have not played for France in the last five years. Going the other way, however, there are no time restrictions placed of French Guiana players playing for France.
Not many people will know where French Guiana is in the world. It is in South America and shares borders with Brazil and Suriname. The country actually shares more similarities with Caribbean culture than South American. As a further twist in the diversity of the country, being an overseas French territory, French Guiana is actually part of the European Union.