Carton was born in Meaux. He received his medical education at the Ecole de Medecine de Paris. In 1903, Carton suffered from tuberculosis. He became disillusioned with the medical establishment and took interest in alternative medicine and vegetarianism which he claimed helped recover his health. Carton was a vegetarian and promoted "naturist vegetarianism".
Naturist vegetarianism was a dieting and health system that involved abstinence from drugs, meat, processed foods and alcohol. It embraced natural hygienic principles, gymnastics, hydrotherapy and prayer. Carton was influenced by Hippocrates and his conception of naturism was entirely opposed to nudism which he equated with moral degradation. He advocated asceticism in relation to clothing, drinking, eating and sex.
Carton was a Catholic and held anti-materialist views. His ideas about naturist medicine were influenced by Catholicism and vitalist philosophy. His dietary principles became known as Cartonianism. There was a religious element to his dietary principles. He believed in original sin, hell and the Christian sacrifice was central to his medical worldview. He held the idea that health should be earned and that pain had a purifying role. Disease was the result of violation of physical and mental laws.
Carton was opposed to the overfeeding of patients. He believed that strict control of eating would allow patients to be cured. He campaigned against the consumption of butter, meat and white bread. He operated a sanatorium at Brevannes, near Paris. The sanatorium had a laboratory for testing his dietary and hydropathic ideas.
In 1921, he created the Societe Naturiste Francaise' (French Naturist Society) and in 1922 the journal La Revue Naturiste (The Naturist Review).