PARIS—The man who killed 84 people in Nice was a violent drinker and drug taker with an “unbridled sex life” who developed a fascination with Islamic State and other terrorist propaganda, prosecutors said as they deepened their probe into whether a broader network fostered his radicalization.

François Molins, the chief Paris prosecutor overseeing the investigation into the Bastille Day attack, said Monday that police haven’t found any evidence that Mohamed Lahouaiej Bouhlel explicitly pledged allegiance to Islamic State or...