Être en nage
It seems that this expression has been misconstrued over time.
Originally, “a nage” meant the action of sailing or rowing. Then it came to mean “by swimming.” In the 16th century, “être en nage” or “être a nage” meant to swim in water or some other liquid.
It gradually took on the figurative sense of “to be all wet” and its accurate meaning now is “to be soaked in sweat.”