A man has reportedly been beheaded in and an Islamist flag “raised” in a France street.
It is understood police found a man’s head with Arabic writing on it.
Witnesses say two attackers drove a car full of gas canisters was driven into the building at around 10am.
Local media are reporting several deaths in the city of Grenobles, near the foot of the French Alps.
French media are reporting a 30-year-old man, known to the authorities, has been arrested in connection with the incident and has claimed to be a member of Islamic State.
Loud explosions have also been heard.
The exact circumstances of the incident are not known at this stage.