Spot on! It's a Latinized version of a Greek borrowing, which is quite
common practice in English.
Was it borrowed first from Greek into Latin and then from Latin into English, or was it borrowed directly from Greek into English but treated as Latin?
It is actually a passive participle in Greek
and is feminine because it agrees with the word for 'day' which, if
context is clear, can be omitted (or "understood"):
hai epagomenai [he:merai] = the intercalated [days]
he: epagomene: [he:mera:] = the intercalated [day]
Ah! In the original Egyptian calendar the epagomenal period was nameless (although the individual days eventually acquired names), but by the time the Copts adopted it the period was treated as a short 13th month named "Epagomene:". That must have originated from referring to them as "epagomenal [day] 1, epagomenal [day] 2", etc., which got re-analyzed with "epagomenal" as the name of the month.