A search is on at Grenoble, where he lives, French dailies Le Dauphiné Libéré and Le Progrés said.
He is now the subject of an international murder warrant.
The man had been seen with the woman, who has not been named, days before the probable date of the crime, they said.
The girl’s body was found earlier this week in a ruined church above La Salle, in the Aosta Valley.
An autopsy Tuesday showed she had bled to death from deep stab wounds to the neck and abdomen.
She was identified by family members, but her name has not been released.
ANSA