A source close to the investigation into the thwarted attack, who asked to remain anonymous, said the four people arrested had been planning to film the decapitation of a member of the military.
Police arrested the four in several places around France – in Bouches-du Rhonee near the city Marseilles, Les Yvelines near Paris and a third location near Lyon.
The statements says investigators identified the “main instigator” in the alleged plot through his “activism on social networks and relations with French jihadists now in prison”.
He had also triggered alarms by signalling his desire to travel to Syria, Cazeneuve said.
France remains on alert six months after attacks in and around Paris resulted in the deaths of 17 people.
Separately, President Francois Hollande said terrorist attacks had been thwarted in recent days, though he made no link with the explosions at the petrochemical plant.
One of the four people arrested had served in the navy, Cazeneuve said.
Mr Cazeneuve said that 1,850 French residents are involved an Islamist extremist activities; 500 of those are now present in Syria or Iraq, he said.
“At the (Bastille Day) ceremony, the President reminded us that every week we prevent… terrorist acts”, Cazeneuve said.
Authorities are still investigating the simultaneous blasts that hit two tanks containing chemicals early Tuesday, setting off huge fires at the plant in Berre-l’Etang, northwest of Marseille, according to CNN affiliate BFMTV. “The first indications show that we are dealing with a criminal act, but no motive has been established”, Cazeneuve told the lower house of parliament.
Tuesday, explosions happened at a pair of petroleum tanks in southern France that officials believe may be terror-related – and possibly linked to the theft of explosive devices from a nearby military camp last week.
Paris has tightened security around sensitive sites such as factories, calling for “maximum vigilance”.
And last month, a man with suspected links to the Islamic State group spiked his boss’s severed head onto the fence of a United States-owned gas factory.
“There is no such thing as zero risk”, said Philippe Prudhon, a technical expert at the UIC union of chemical industries.