What impact did the letter have?
Was the arrival of the sister's letter the catalyst for subsequent events?
Jeanne remarks to Sylvain that she does not know how to reply, indicating that she must have been thinking about the letter at some point. The letter may even have distracted her to the extent of forgetting to check on the potatoes.
The letter's breezy style, interestingly interpreted in its oral rendition, portays a life of comparative excitement (learning to drive!) and luxury (the cousin has his own bedroom!); a life that is glaringly at odds with Jeanne's own existence. The conversation with Sylvain about his father further emphasises dissimilarities in her sister's life from WWII onwards.
Could the receipt of the letter, and Jeanne's brooding upon its contents, have been part of the reason behind her orgasm?
Was it the banality of the contents of the (care?) package, when considered against her sister's lifestyle, that precipitated Jeanne's final actions.
It seems so to me but this aspect does not appear to have been considered yet on this site (or any others I have explored).
That wasn't very sporting, using real bullets.