Spared by the Adaptation: Generally, stories involving Br'er Rabbit and Br'er Fox end with Fox getting caught in his own trap and dying, which naturally doesn't happen here. Granted, he would always return for the next tale.
Villainous Glutton: For someone so thin, he is very obsessed with cooking Br'er Rabbit. Though it must be said that it is more about pride and hatred than food as he was willing to forgo a meal if that meant he would give Br'er Rabbit the worst fate he could think of.
Bears are Bad News: If you happen to be a potential meal or cause of irritation for him watch out
Beary Funny: He is so stupid it is amusing and also has a playful and lighthearted side in him.
Dumb Muscle: The muscle is the only thing he is using and he's too slow to realise any obvious tricks unti the Fox plainly points them out.
He could also be a subversion, since in the end he actually DOES step forward and save the day.
Nice Guy: He's the only character in the movie to not be shown having any real character flaws or being rude to people at any point. Given that the movie was trying promote tolerance, this was probably intentional.