ACtually, lingua franca was NOT French. Also known as _sabir_, it was a pidgin language used by the sailors in the Mediterranean (it went extinct in the XIX century). It was a mix of various romance languages and Arabic and Turkish. At first the main romance language mixed was French, then the influence of Spanish and Italian become more notable. The name was coined by the Turks (for whom people speaking romance languages must have looked similar enough to call them all "Franks").
I agree. What acutally the lingua franca was, changes from time-period to time-period and location. And you're right, what the part "franca" in lingua franca refers to is the Franks, but so does french ;-)
I don't mean that at all times and at any place people spoke French to foreigners. It has been Latin before French, it is English ever since. And the term lingua franca just happened to come into existence while french/frankish was the no 1 language or the "Franks" the no 1 nation in western europe.
Sabir was a pidgin language, but calling it the lingua franca would not satisfy me. Since surely no one sailing from helsinki to stockholm back then, spoke even a dime turkish. Lingua Franca, at least for me, refers to what original language non-native speakers are driven to to speak in. Thus creating pidgin languages.
E.G.: Back then Danes or Swedes did have no intention to use arabic even when meeting an arab trader in some port, since it was easier to try it with some frenche verbes.