The reel has nothing at all to do with the song, beyond a coincidence of title. The 'Royal Charlie' Joyce intended was the jig of that name (Joe has provided a link to examples at JC's Tunefinder). As sung nowadays it has changed a bit, but is still recognisably the same tune, albeit altered. Here is an example as printed in the late 19th century (though from a reprint of 1922):

X:1
T:The Wind that Shakes the Barley
C:Robert Dwyer Joyce (words)
N:Tune: Royal Charlie
B:A P Graves, 'The Irish Song Book'. London: T Fisher Unwin, 14th impression, 1922, 70-71.
B:First edition 1894.
M:6/8
L:1/8
Q:1/4=100
K:C
"mournfully" B|c2 A (AG) E|c2 A (AG) E|c2 A d2 B|G3 (GA) B|
w:I sat with-in_ the val-ley green_ I sat me with my true love_ My
c2 B c2 d|(ef) e e2 d|c2 A (BA) G|A3 A2 B|
w:sad heart strove the two_ be-tween The old love and_ the new love The
c2 B c2 d|(ef) e e2 d|c2 G (cd) e|(d2 B) (GA) B|
w:old for her, the new_ that made Me think on Ire_land dear-*ly_ While
c2 B c2 d|(ef) e e2 d|c2 A (BA) G|A3 A2||
w:soft the wind blew down_ the glade And shook the gold-*en bar-ley.