Why does Renge cosplay as Kisaragi Quon?
In the designs created by Akihiro Yamada, that were adapted by Hiroki Kanno for the anime, Quon is depicted wearing clothes with a very French motif (e.g. parasol, beret). 



On the Vol.2 DVD release (used in France and Japan, but not in the initial U.S. and UK release), Yamada illustrated Quon wearing a frilly lace-trimmed dress and stockings, carrying a parasol for a goth loli look, which was inspired Old French Victorian style dresses.



The stereotypes mesh well with Renge, being a French "otaku."