A Francophone is a person who speaks French natively or by adoption (i.e., the person uses it in everyday life). As an adjective, it means French-speaking, whether referring to individuals, groups or places.
Francophone countries include France, Belgium, Canada, and Switzerland, Haiti and the French West Indies, and several countries in Africa that are former French colonies. Collectively these countries are known as the Francophonie.
A related term is anglophone, which means English-speaking. In Quebec, the term allophone has also been coined, and means "has a native language other than English or French". All three words have crossed over into Canadian English, and are politically charged to some extent.