The answer is Florida. It is the one in that set that is not derived from French; Louisiana, Vermont, and Arkansas all have French-related etymologies.

Why

  • Louisiana comes from French Louisiane.
  • Vermont is generally traced through French vert mont / “green mountain.”
  • Arkansas comes through French spelling and pronunciation of a Native American name.
  • Florida is Spanish in origin, from La Florida.

In one line

So, if the choices are Louisiana, Vermont, Arkansas, and Florida, the one that isn't derived from French is Florida.