'Racket' is actually the older of the two words. Here's a brief history of the earliest recorded appearances...rakkett (1500)...raquet (1540)...racket (1690) and racquet 1828.
probably courtiers trying to convince themselves they were playing a posh game by spelling it French. It was still court tennis in those days I think; lawn tennis came in in the 1870s approximately, and was called sphairistike until someone saw sense. I think racquet has been on the retreat for 20 years or more.