The "J" spelling of Gevaudan/Gevedann/Gividen/Gividon, etc. arose, as nearly as I can determine, in western Virginia/West Virgina where, since so many of the county clerks were illiterate or functionally illiterate, in order to have the name pronounced with the soft French G rather than the hard Germanic/English G, the family just went ahead and spelled the name with a J, which is always soft in English.
That's my theory anyway. If anyone else has a theory, I would be interested in hearing it. As far as I can tell, most of the family, outside WV, still spells the name with a G to this day. (If you want to locate ALL your lost cousins you always have to look in the G section of the phone directory as well as the J section).