"light carriage with low wheels either open or covered with a folding top," 1660s, from French calèche, from German kalesche, from Bohemian koleska, diminutive of kolesa "wheel-carriage," from kolo "wheel," from PIE root *kwel- (1) "revolve, move round." Also the name of the folding hood or top fitted to it (1856).
The Caleche is of French origin; a carriage with leather top, and portable glass shutters on the sides, and a panelled front, with sliding window. The whole front may be removed in a few minutes, making it an elegant open Barouche, with a half-top over the back seat. [Henry William Herbert ("Frank Forester"), "Hints to Horse-Keepers," New York, 1859]