French police on Saturday interrogated the suspect in the attack, Yassin Salhi, a 35-year-old deliveryman and married father who officials say drove his truck into the American-owned Air Products factory in the town of Saint-Quentin-Fallavier, close to Lyon. He set off an explosion and mounted the head of his boss onto the gates of the plant.
The head was "hung onto the fence surrounded by two Islamic flags bearing the Shahada, the profession of (the Muslim) faith," French prosecutor Francois Molins told news agency AFP.
It is the first time someone in France has been found beheaded by a suspected Islamist extremist.
The attack comes nearly six months after the terrorist attacks in and around Paris that killed 17 people in January, starting with a shooting at the offices of French satirical magazine Charlie Hebdo.
French President Francois Hollande has ordered security tightened to the highest possible level in the region ahead of a second emergency meeting of key ministers due to be held Saturday.
Valls told AFP that Friday's attack would create tension in France that "will be exploited".
"It's difficult for a society to live for years under the threat of attack," he said Saturday on a flight back to France from Bogota, adding: "The question is not ... if there will be another attack, but when."
Salhi was known to security services for a number of years and had been investigated for links to radical Salafists but had never been identified as planning an attack, Interior Minister Bernard Cazeneuve told reporters. He did not have a criminal record.