Regional newspaper Nice Matin quoted its own reporter at the scene saying there were many injured people and blood on the street.
BFM TV said at least 30 were dead after the truck drove through people on the famed Promenade des Anglais on the Nice seafront.
BFM said local authorities were treating the incident as an attack. Almost exactly eight months ago Islamic State militants killed 130 people on a Friday night in Paris in November.
"Dear Nicois," local government leader Christian Estrosi wrote in a tweet. "The driver of a truck appears to have killed dozens of people. Stay at home for the time being. More news to follow."
Regional newspaper Nice Matin quoted its own reporter at the scene saying there were many injured people and blood on the street.
It published a photograph of a damaged, long-distance delivery truck, which it said was "riddled with bullets" and images of emergency services treating the injured.
Damien Allemand, the paper's correspondent, was quoted as saying: "People are running. It's panic. He rode up onto the Prom and piled into the crowd ... There are people covered in blood. There must be many injured."