I doubt it comes from
Yvette, the root work is too different. If anything I think it's related to Abeille (
Bee in french)
"The Latin apis had created the word ef ("bee") which in turn has created a diminutive avette ." - I think this is used in the South of
France more than anywhere else but I can't be sure.
Translated from:Le latin apis avait engendré le mot ef (« abeille ») qui à son tour a engendré un diminutif avette.
http://fr.wiktionary.org/wiki/avette