It's currently unknown how Francisco became a D.O.O.M. agent, but from his accent and according to Butch Hartman, he's from Chicago. Ollie and Larry are not as evil as he is, and he cares about Snaptrap, even though he has laughed at him a few times.
Francisco also seems to have a bit of a dark side to his personality, as seen in Forget Me Mutt, when Snaptrap asked for ideas on how to defeat T.U.F.F., he suggested that they eat them, to which Snaptrap said that that was just "dark and disturbing." This is most likely because he is an alligator, which are well known for being vicious and eating many different animals.
Even though Francisco is one of the more evil characters in the series, he usually enjoys hanging out with his friends, whether they're on missions to do missdeeds, or just doing something for fun, such as playing games and eating ice cream.