>EDIT: Latin: "papilionem" (papilio?), so at least French and Catalan have conserved it, and I can see that Italian "farfalla" could be cognate.

Sure, "farfalla" is relatively recent, in old italian it is "parpaglia" or (still used in some dialects "parpaja" or "parpajon"), according to some sources:

http://www.etimoitaliano.it/2017/02/farfalla.html

There is seemingly an Indo-european root "s-par" or "s-pal" or "s-far" and the Greek "pallo" with the meaning of something that vibrates.

The root seems the same a "palpebra" (eyelid) which is paupière in French, párpado in Spanish and pálpebra in Portuguese.