The shootings took place late Thursday afternoon at the family home in the quiet Alpine village.
The teenager was hit in the head and was transported in a coma to hospital in Grenoble, according to the Le Parisien newspaper.
The man's mother, who was also subjected to an attack, managed to evade the gunfire and call the emergency services for help.
The 23-year-old was arrested at the family home and taken away for questioning by police in Albertville. His brother will be questioned if and when he awakes from his coma.
Little is known of the background to the attack. The newspaper reports only that the father worked within the construction industry and that there was ongoing tension with his eldest son.
A handgun is reported to have been recovered at the property.
The attacks took place on the same day as the funeral in Auxerre of a mother, grandmother and two children who were killed in their sleep by their father last week before he committed suicide.
While the investigation into the deaths is ongoing, it has been reported that the father was having trouble at work.