There is not a lot of plot to this story.
The narrator reads the story of a murder-suicide and that reminds him of a time that he went hunting with his cousin who lives out in the country.
The narrator spends a lot of time talking about the marshlands where they are going hunting and about how that landscape makes him feel. Then he describes their duck hunt. The narrator shoots a female duck. The male duck will not leave the area because he misses his mate. When he comes to investigate, the cousin shoots it.
The narrator then puts the ducks in the game bag and says that he goes back to Paris the same evening.