Yes they are pronounced the same way.
Aimee (without the accent) and
Amy. However, with the accent, Aimée, is pronounced eh -
MAY.
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In valley green or towering crag
Our fathers fought before us,
And conquered 'neath the same old flag
That's floating o'er us,
We're children of a fighting race
That never yet has known disgrace,
And as we march the foe to face!