I don't know it so I had a listen online and it's in a MINOR KEY.
Your chords, with capo on the first fret, mean that your arrangement is in the key of F minor. The flute player can't be playing in C - she must play in F minor too - or else you must reposition your capo to suit whichever minor key she's going to play it in. (It's much easier for you to change key than her.)
Edit: Just a thought. Why did you think it was written in C? Is it because there are no sharps or flats in the key signature? In that case it's in A minor (the relative minor of C major). If you want to play those chords you mentioned in A minor, then you need to put the capo on the fifth fret, not the first.
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