In Lingua Franca (the specific language), lingua is from the Italian for ‘a language’. Franca is related to Greek Φρᾰ́γκοι (Phránkoi) and Arabic إِفْرَنْجِي (ʾifranjiyy) as well as the equivalent Italian—in all three cases, the literal sense is ‘Frankish’, leading to the direct translation: ‘language of the Franks’. During the late Byzantine Empire, Franks was a term that applied to all Western Europeans.
So if anything, it’s (roughly) Italian, Greek, and Arabic for “language of the Western Europeans”.