E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
A purse. Hence, a young boy thief is called a Raton. A sort of pun on the word rapt from the Latin rapto, to carry off forcibly. Courir le rat, to rob or break into a house at night-time.
To take a rat by the tail, or Prendre un rat par la queue, is to cut a purse. A phrase dating back to the age of Louis XIII., and inserted in Cotgraves Dictionary. Of course, a cutpurse would cut the purse at the string or else he would spill the contents.