I'd think of it as being in Am with accidentals on the E major chord. But that might just be me.
Notes of Am = A, E, C
Notes of G = G, B, D
Notes of F = F, A, C
Notes of E = E, B, G#
The scale you'd be playing on for the most part would be
A, B, C, D, E, F, G, G#,
I'd say the key is Am.