Lingua franca isn't just a gussied up way to say pidgin language, and Creole is not limited to languages of French ancestry. So what's the story behind those terms? Let's take a look.
The first known lingua franca—literally, "Frankish language" in Italian—was spoken in the medieval ports of the Barbary Coast and the Levant. That original Lingua Franca was based on Italian and included elements of French, Spanish, Greek, and Arabic. It proved so handy, its definition was broadened to include any language used as a common or commercial tongue among peoples of diverse speech. Need an example? French was the language of choice (and the lingua franca) of 18th-century diplomats.

If lingua franca names the language used by folks who have no other language in common, pidgin names the lingua franca whose grammar and vocabulary have been sharply reduced. The term pidgin has its origin in the Chinese Pidgin English word for business; as you might expect, Pidgin English was first spoken in the Orient.

When an entire speech community gives up its former language or languages and adopts a pidgin as its mother tongue, that pidgin is said to have been "creolized." Appropriately enough, the Portuguese ancestor of Creole meant "person of European or African descent born in the colonies"; various Creoles are spoken not only in southern Louisiana but everywhere—from Haiti to Hawaii.