There is one joke in this slapstick from Jean Durand's comedy unit at Gaumont: Calino wants to win a boxing match, and decides that he needs to toughen up one part of his body: no glass jaw for him! So he subjects his chin to various punishment, all of which he endures with no sign of discomfort.
Bout de Zan is a young boy by description and a petty thief by vocation. In this short, he does indeed steal an elephant from a circus, parading it around town and using it to beg for money. Due to their rambunctiousness, Bout de Zan and the elephant (!) need saving from the authorities.
Remember when Julie Andrews in The Sound of Music says "Every time God closes a door, He opens a window?" Well, this is basically the same philosophy followed by a sage authority named Professor Azais. Though he is never seen in the film, Azais's influences dictates every move made by Le Baron...