Most French cities have a Rue de la Soif but you'll never see it written on a street sign. It literally means "thirsty street" and is more of description of the clientele and businesses than it is a proper name.
If you are on the Left Bank in Paris and somebody directs you to a restaurant or bar on Rue de la Soif, head over to Rue Guisarde. It only stretches one long block so it's tricky to find the first time but you'll know it when you see it! As a bonus, you'll also find a little art project by Invader on the wall at the entrance to the "Rue."