The medieval pheasant was very likely the Common Pheasant, Phasianus colchicus. This bird is also sometimes refered to as the English Pheasant. Introduced by the Romans to England where it was kept as a game bird, but died out when they left. Reintroduced in approx. the 10th century (or by the Normans) it was hunted to extinction in the 17th century and then reintroduced in the late 19th century.
The male is around 50 to 70 cm in length plus tail. The female is has a much duller plumage than the male.
Medieval legend has it that the cock may become entranced by its own image and thus may be captured using a mirror.
Phillip the Good of Burgundy made a "Vow of the Pheasant" in 1454 to rescue Constantinople during the Third Crusade. He failed.