Final answer:
Dupin deduces the French sailor's ownership of the orangutan by employing unconventional thinking and understanding of human behavior, setting him apart from the police's standard investigative methods.
Step-by-step explanation:
In the story, Dupin figures out that the French sailor owns the orangutan through a combination of astute observation, logical deduction, and a thorough understanding of human nature and behavior. Dupin's method involves considering possibilities that the police might overlook because their methods are based on their own ideas of ingenuity, rather than that of the individual they are pursuing. By not confining his thoughts to the conventional, Dupin is able to piece together the unusual circumstances and connect the sailor to the orangutan.