KERLÉGO, France — A dairy farmer, Jean-Pierre Le Guelvout, once kept 66 cows at a thriving estate in southern Brittany. But falling milk prices, accumulating debts, depression and worries about his health in middle age became too much to bear.

Just 46, Mr. Le Guelvout shot himself in the heart in a grove behind his house one cold December day last year. “It was a place that he loved, near the fields that he loved,” explained his sister Marie, who said she was “very close” to him but did not see his suicide coming.

The death of Ms. Le Guelvout’s brother was part of a quiet epidemic of suicide among French farmers with which stoical rural families, the authorities, public health officials and researchers are trying to grapple.

Farmers are particularly at risk, they all say, because of the nature of their work, which can be isolating, financially precarious and physically demanding.