Yet Mr. Marot’s rudeness, bad temper and propensity for violence were an open secret.

“Those kinds of things stay behind closed doors,” said a local man at the only bar in town, Le Bar de l’Amitié, or the Friendship Bar, who asked to remain anonymous because he had had problems with Mr. Marot in the past.

Behind those doors, Mr. Marot physically and sexually abused all three of his daughters when they were teenagers, the daughters testified, and also hit Pascal, their brother. Ms. Sauvage did not know it when she killed her husband, but Pascal, 44, committed suicide the day before.

Court documents show that Ms. Sauvage and her children felt constantly threatened by Mr. Marot, who told his wife that he would kill her and her children if she tried to leave.

Ms. Sauvage once tried to kill herself, but a doctor who treated her never inquired about the reason. When her daughter complained to the police that her father had raped her, the local police officer, instead of taking her seriously, called Mr. Marot, prompting her to retract her accusation out of fear of her father’s reaction.

Catherine Le Magueresse, a researcher who specializes in violence against women, said the Sauvage case raised questions about French institutions’ failure to help battered women. “The justice system is not trained for such cases,” she said, “and the phenomenon of physical and psychological hold is not well known.”

But, she added, “Everyone in feminist circles and in the justice system were not at ease with this case, because when you are a victim of physical abuse and you kill your abuser, you become like him in a way — you choose violence.”

France first recognized domestic abuse in its penal code in 1992, and it has adopted a range of measures in recent years to tackle the problem. Training on violence against women became mandatory for doctors and midwives in 2013, and a free national phone line was set up in 2014. More training for police officers and social workers is planned.