Counter-terrorist investigators were leading the probe, into the attack, local media said, and a local government official said weapons and grenades were found inside the truck.
Police shot and killed the driver, who drove the 25-tonne, unmarked, truck for well over 100 meters along the famed Promenade des Anglais seafront, slamming into a mass of spectators late in the evening, regional government official Sebastien Humbert told France Info radio.
The man had opened fire on the crowd, local government chief Christian Estrosi told local media, also citing the discovery of weapons and grenades after the driver was killed.
"It's a scene of horror," a local member of parliament, Eric Ciotti, told France Info. He said 80 people were dead after the truck sped along the pavement fronting the Mediterranean, before being stopped by police after "mowing down several hundred people."
"People went down like ninepins," Jacques, a restaurant owner on the seafront Promenade des Anglais, told France Info.
Local newspaper Nice-Matin posted photographs of the truck, its windshield starred by a score of bullets and its radiator grille destroyed. Since Islamic State attacks last year, major public events in France have been guarded by troops and armed police, but it appeared to have taken some minutes to halt the progress of the deadly truck in Nice.
Nice-Matin quoted officials as saying 42 people were in critical condition. Many others were less seriously hurt.