This would make a lot of sense in french, since the words “verre” (glass) and “vair” (on uncommon and old word refering to a kind of fur) are pronounced in the same way, so the mistake could have been easily done, story tellers mistaking one rare word for another much more common.
However, why would the same mistake be done in non french versions of the tale?
Actually, the earliest version (Giambattista, again) says it’s a pianelle which “Cinder-Cat” loses. They were a sort of galosh which protected the shoe from the mud-- the overshoe rests on a foot-tall stilt with a wide circle base. (They’re also known as *chopines. *
Here are some images of them, and a page that discusses their use.
Giambattista’s stories may be the earliest written versions of many fairy tales, but there is no reason to suppose that they’re “original” in the sense of being closest to the oral history versions.