Following up on Virginia's thoughts about the derivation of "josey" from "Joseph"....

In Elizabeth McClellan's "Historic Dress in America", she describes two new warps that have come into fashion in 1848, a "Cornelia" and a "Josephine" (pg. 452):  "....and the Josephine mantle with one cape, without shoulder seams, reaching to the waist, were popular favorites."  

Your Louisiana provenance might also explain the "French connection."

Look forward to learning the "final answer."