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.