A closer traduction could be "drunkard", since "saoûl" means "drunk" in French. The construction is the same : s(a)oûl-ard, drunk-ard.
Note that unless said jokingly, the word "saoûlard" strongly implies that the person in question is alcoholic, or at least regularly gets drunk. In my knowledge, it is almost never used to describe someone who just happens to be inebriated. Its more common, less "strong" synonym "ivrogne" is more ambivalent, however.