Authorities are not yet clear as to what drove the suspect, 37, to attack the mother and her three children aged eight, 12 and 14 at the resort near to the town of Laragne-Montéglin, in the country’s Hautes-Alpes region.
The attacker, from the Paris area, was staying with his wife and children at the same complex.
Following the incident, the deputy mayor of Laragne-Montéglin, Jean-Marc Duprat, said the attacker had been upset with the family for wearing shorts and T-shirts, The Guardian reports.
His comments were later retracted with the man’s motive not known.
Prosecutor Raphaël Balland, said the reasons behind the attack were “very hazy” and believed the theory of the assailant attacking his victims for what they were wearing to be a “rumour”.
He also added that the man had “not uttered any words reproaching them for their dress at the moment of the attack”.
A police source told French newsmagazine Nouvel Obs that “No words of a religious connotation were uttered.”
According to local newspapers, the youngest victim was helicoptered to hospital in Grenoble following the attack with her condition said not to be life threatening.