"Francophone" (literally "French speaking") is the term currently in use in the US and elsewhere to designate literatures written in French eminating from writers and scholars in former French colonies around the globe. The term, as well as the concept it designates, speaks to a complex relationship among the French speaking people in these countries both to the rest of the population (often speaking other languages), the French speaking world at large. It also incorporates the historic colonial history of these region to the country of France.
These and other themes are explored in many of the websites and resources listed in this guide.
Like the terms "Near East" and "Far East," or "Orient," (near, far, and east of what?), the term "Maghrib (also "Maghreb") is a particularly ethno-centric term. It derives from Arabic, and means "west," or "place of sunset." In its broadest sense, it generally refers to the North African region comprising the countries of Morocco, Algeria, Tunisia, Tripolitania, and sometimes Libya.
If you imagine what country you would need to be standing in to look west out onto these countries (not Europe, or any of those named), you would be right if you guessed "Saudi Arabia." The Arabs conquered this region between 643 and 711 AD, and ruled it until it was conquered by the Ottoman Empire. France colonized this region betweeen 1830 and 1912. Most countries in this region won their independence in the early 1960's, with Libya--once a colony of Italy, then governed by France and Britain--achieving independence in 1951.
(1) Bibliographie du Maghreb Antique et Médiéval