Enharmonic equivalency of the French sixth Augmented sixth chord

the french sixth has 2 characteristics in common diminished seventh chord:

as diminished seventh chord, latter property allows chord used in modulating remote keys. instance: ♭6–1–2–♯4; (a♭–c–d–f♯ in c), interpreted identically in f♯ if reordered , respelled d–f♯–g♯–b♯, i.e., french sixth of ♯iv key area, displaced interval of tritone relative tonic key, i.