This is a trifle embarrassing, and for once we have no idea to start. We know “lick” means to pass the tongue over something in order to taste, moisten, or clean it. It also means to defeat something comprehensively. We are clutching at straws. What or who was “French”. To make things more complicated, basketball star Larry Bird’s hometown is French Lick too. Possibly, he licked the competition there although we’re only guessing.
It seems the French like salty things and so do steers. They once charged per cow to let them lick the ground (stranger things have happened, folks). Later Al Capone stopped by to try his luck at the Casino. That’s about all folks, and oh boy we can just imagine the tongues going lick, lick, slurp.