My understanding is that "franca" in this context means "franche = libre" in french, "free" in english. Meaning, a common language at disposal of all to exchange. Like in "ville franche" in Middle Age, and "zone franche" today.

The root is the same as for the Frank tribe, the "Free Men" in old Germany (remains of tribes defeated by Rom, who, to stay free, united in swampy areas of Belgium, and ultimately created the kingdom of Franks).

It could also derive from "Franj" (Frank) used by all Byzantins and Arabs to name the western europeans and their linguages, be them french, german, british, italian or spanish.