I do not think that there is probably anything that he could have done. After all, no one believed him even after the wallet had been found and returned.
However, the one thing that might have helped him would have been if he had explained how long he and Malandain had hated each other. This would have explained why Malandain would have accused him falsely. It would also have allowed him to explain why he kept looking around on the ground.
Maybe if he had explained this, he could have turned the tables on Malandain and gotten him in trouble for false accusations.
The fault of Maitre Hauchecorne of Guy de Maupassant's "The Piece of String" is his pride, and it is this pride that makes him hide his act of having been so "thrifty like the true Norman he was" when his rival, Maitre Malandain, the harness maker witnesses his stooping:
Maitre Hauchecorne felt a bit humiliated at having been seen by his enemy scrabbling in the dirt for a bit of yearn. He quickly thrust his find under his smock, then into his trousers pocket' afterwards he pretended to search the ground for something he had lost, and at last he went off toward the marketplace with his head bent forward and his body doubled over by his aches and pains.
Then, the tragic mistake that Hauchecorne makes in his pride, is not admitting what he has really done when the police sergeant questions him:
'Maitre Hauchecorne...you were seen this morning on the Beuzeville road picking up the pocketbook lost by Maitre Houlbreque, of Manneville.'
'Me? Me? Me pick up that pocket book?....I swear! I don't know anything at all about it.'
'You were seen.'
At this point, were Maitre Hauchecorne to admit that he bent to pick up a piece of string, he may have been able to redeem himself, especially if he explained why and had witnesses to testify to his habitually frugal nature. However, the first action of trying to dissemble what he was doing as he stooped in order to deceive M. Malandain was probably the cause of the lack of credibility in anything that M. Hauchecorne declares after this.
In his story, Maupassant presents the natural distrust of the peasants for one another; also, as he expressed in his story "The Necklace," Maupassant implies, "How small a thing is needed to make or ruin us!" So, perhaps, there may have been nothing M. Hauchecorne could have done because of the suspicion with which the peasants regard one another. After all, they still suspect M. Hauchecorne even after the wallet is found. Nevertheless, his lies are certainly his further unraveling, for in his desperate attempts to regain his credibility, he is mentally destroyed as well as socially.