Une chaussée is another word for "road," and rez is Old French for ras, meaning "flat" or "level" (think of the word "razor"). The ground floor is called le rez-de-chaussée in French because it is level with the road.
It's kind of cute, but I think you mean "chauseé" and not "chausette". Chausée is an old word for road that has connections to German. "chausette means "socks" :) Kind of a cute picture though...... "sock level" instead of "street level".