Not all nicknames are derived from a person's given name - maybe the character goes by their last name or middle name, or a nickname that isn't related to their name at all.
But if you want the nickname to come from Versailles, maybe
Vera or Ersa /
Ursa? Or just V / Vee (although that's maybe too associated with V for Vendetta?)
Also, I'm curious - is the association with the palace something you like about the name?
"The trouble with having an open mind, of course, is that people will insist on coming along and trying to put things in it." -
Terry Pratchett