Private First Class Cedric Cordier was approached from behind and stabbed in the neck with a small-bladed knife.
Defence Minister Jean Yves Le Drian told reporters that he had been targeted because of his profession.
But President Francois Hollande refused to make any direct link with the murder of a soldier in London on Wednesday.
Two men arrested on suspicion of murder at the scene of the London attack remain in custody in hospital in a stable condition. Michael Adebolajo and Michael Adebowale were shot and wounded by police.
On Saturday, British police arrested three other men on suspicion of conspiracy to murder the soldier, Drummer Lee Rigby, who was not on duty. A sixth man was arrested on Thursday.
Meanwhile, the Kenyan government denied allegations that its security forces had abused Mr. Adebolajo, insisting he had never been there.
Photographs of him in a courtroom in Kenya more than two years ago have been published. He is alleged to have been arrested for seeking training from the Islamist militant group, al-Shabab, in Somalia.
In Saturday’s attack in Paris, Pfc Cordier was on patrol with colleagues from the 4e Regiment de Chasseurs de Gap and police officers at La Defense’s metro and train station, when he was approached from behind and stabbed in the neck with a knife or a box-cutter.