Fanne was an obsolete term for a female fan dating from the days when there weren't very many. It didn't survive, being replaced pretty universally by femmefan in the 1960s, tho it lasted a bit longer than firl.

from Fancyclopedia 2 ca. 1959
(pronounced "fan"). A female fan; also femmefan. Nancy Share tried to introduce Firl, but this didn't catch on. Feminine objection to this term is caused by clods giving the silent E full value (of Fanspeak).
from Fancyclopedia 1 ca. 1944
Pronounced same as "fans", but used in written to mean fem fans.