When old Maitre Hauchecorne retrieves a discarded piece of string from the street near the Goderville square, little did he know that it would lead to a personal humiliation that would follow him to his grave. The conflict of the story arises when Hauchecorne's adversary, Malandain, witnesses Hauchecorne pick up something from the street. Later, it is discovered that another man, Houlbreque, has lost his purse in the same vicinity. Malandain accuses Hauchecorne of the "crime" of finding the purse, which Hauchecorne vehemently denies. Although the purse is eventually found, Hauchecorne's continued pursuit of redemption from everyone he encounters works against him. People assume that Hauchecorne's neverending explanations are meant to cover up a second person's involvement. Hauchecorne is an innocent man, but his past reputation marks him as guilty to nearly everyone in town. He dies with this unfounded accusation haunting his final words.
The first conflict is the lack of trust: namely between Hauchecorne and Malandain, then Hauchecorne and the mayor. But, eventually, the reader sees that it is a lack of trust amongst/between all the peasants themselves. Guy de Maupassant had a similar view about the peasantry: that they were untrustworthy. Being from a higher class, he may have prejudged these people, not thinking their craftiness and treachery is the result of a struggling economic class. As Hauchecorne makes his way through the marketplace, the narrator says:
The peasants milked, went and came, perplexed, always in fear of being cheated, not daring to decide, watching the vender's eye, every trying to find the trick in the man and the flaw in the beast.
The other conflict is Hauchecorne's own pride. It seems that Maupassant makes it a point to note that the Norman peasants were economical to the point of being stingy. So, for Hauchecorne to be so intent on proclaiming his innocence, he's playing a futile game. The other peasants view him as a thief, but the point Maupassant tries to make is that the peasants do so, knowing they'd probably have stolen the wallet if they had the chance. I guess the overall conflict is the corrupt socio-economic system that led to a culture of backstabbing peasants.
Hauchecome may have his own set of defects; after all, no one is perfect. So, it is totally unfair to blame him for his eventual "downfall", pathetic this downfall may be. Rather, it was the people's cruelty that led him to this fall. He died pursuing his innocence and protecting his public reputation to no avail. But his death was more of an indictment of the society's insensitivity and cruelty rather than Hauchecome's egotistical pursuit of his reputation. Yes, he was so resolute in defending himself before the people that the these people misconstrued his overly-defensive stance. And this is where the conflict lies --- Hauchecome's naivete struggling against a much stronger evil forces of a decadent society that he lived in. The society that conscripted and conspired him to his deathbed. He did what he thought was the right thing to do but the cruelty of the society was too much for him to bear that it took a toll on his physical and mental health. He died pursuing his public repute to no avail.