Fey Ancestry does not confer resistance to Madness
You have advantage on saving throws against being charmed, and magic can’t put you to sleep.
Unless the madness was inflicted as a charm effect, there's no reason to give advantage on the basis of fey ancestry.
Any other resistance to Madness would be related to how Madness was inflicted upon the creature / character. Anything that grants advantage on the save isn't against Madness, per se, but the means by which Madness is being inflicted. (Typically, a spell or a curse).
Going Mad(SRD p. 206)
Certain spells, such as contact other plane and symbol, can cause
insanity. (snip) Diseases, poisons, and planar effects such as psychic
wind or the howling winds of Pandemonium can all inflict madness.
Some artifacts can also break the psyche of a character who uses or
becomes attuned to them. Resisting a madness‑inducing effect usually
requires a Wisdom or Charisma saving throw.