The word is a two-layer etymology puzzle. The Germans call a refugee a Flüchtling -- a word in which the curious will see the diminutive ending -ling and the root Flucht or flight.
Our word refugee has the prefix re- meaning "back to" and a root based on the Latin verb fugere meaning "to flee" (think fugitive or centrifugal meaning center-fleeing). But the verb also means to fly or to take flight: Tempus fugit