What could shoes possibly have in common with a food item made of pizza dough stuffed with cheese and other fillings? Etymologically, quite a bit. Retrace the footprints of both "chaussure" and "calzone" (a word that, like the tasty turnover itself, comes from Italy) and you'll arrive at the Latin word calceus, meaning "shoe." "Calzone" is the singular of "calzoni," which means "pants" (someone must have seen a similarity between the food and the clothing item). "Calzoni" in turn comes from "calza," which means "stocking" and descends ultimately from the Latin calceus. "Chaussure" made its way to English via Anglo-French rather than Italian (and goes back to an Old French verb meaning "to put on footwear"), but it too can be traced to "calceus."
Middle English chaucer, from Anglo-French chausure, from Old French chaucier to put on footwear, from Latin calceare, from calceus shoe — more at calzone