Apparently, German Geflügel “poultry, fowl (birds)” derives
from late MHG gevlügel(e), under the influence of der Flügel, "wing," from MHG gevügel, from OHG gifugili = collective formation, from fogal, "bird".
So if it hadn’t been influenced by the false friend along the way, it might have ended up as Vogel “bird” vs. Gevögel “poultry; fowl”. (Though that second word does exist in German [as a shortening of Gevögele?], albeit with a rather different meaning….)
Still, Geflügel originally related to Vogel. Whodathunkit. Makes sense, though.