Quick look and I see in my Win10 User folder:
  • C:\Users\<WINDOWS_USER_ACCOUNT_NAME>\Documents\My Games\FINAL FANTASY XIV - A Realm Reborn
FFXIV_CHARA_01.dat
And 14 more of these, using the sequential number after the "CHARA_" part of the file name.
I happen to have 15 saved Character Appearance on my computer, so I would say these are it.