The story
First attested in the 1550s, initially in the spelling sergreant, of obscure origin and variable meaning: examples from the 15- and 1600s apply it not only to winged quadrupeds but also a falcon, and not exclusively to ones rampant but also some passant. The source may be French s'érigeant (“erecting itself”).
Etymology from Wiktionary, CC BY-SA 4.0.