This is badge of the 3rd Zouave Regt, a French Colonial unit from North Africa. During WWII they fought along- side the 2nd Bn 503rd Prcht Inf Regt (PIR) and as a result the 2/503rd was authorized to wear the badge.
When the 2/503rd was re-designated the 509th Prcht Inf Bn (PIB) authority to wear the badge was transferred to the 509th which is still authorized to wear the badge today. 1 5.16 in diameter, this badge is a reproduction of a very older version and therefore rather hevay , not the thin copies made today.