A van driver who was investigated for links to Islamist radicals has attacked a gas factory near the south-eastern city of Lyon, a French prosecutor says.
Yassin Salhi, 35, caused an explosion by ramming his car into an area containing flammable liquids and was arrested at the scene, Francois Molins said.
Mr Salhi's boss, the owner of a delivery firm, was found beheaded alongside flags containing Arabic inscriptions.
The attack put France back on to its highest terror alert.
An investigation has been launched by French anti-terror police.
Day of attacks
The attack in France comes on the same day as:
Yassin Salhi drove his van into the Air Products factory in Saint-Quentin-Fallavier, some 40km (25 miles) from Lyon, at just after 09:30 (07:30 GMT).
He was waved through by staff who recognised him as one of their regular delivery drivers, Prosecutor Molins said.
At the scene: BBC's Imogen Foulkes
It began as an ordinary working day, on an ordinary industrial estate in an ordinary French town. People were going about their business in their usual way. But just after 09:00 the day changed.
An explosion was heard from the Air Products plant. Police and firefighters found a half destroyed car which had been rammed into canisters containing chemicals, then a man trying to ignite more canisters.
He was soon arrested, but they also found a decapitated body - the head some distance away - impaled on railings.
When the very first journalists arrived from Lyon, the head was still there. Now the bland anonymous roads of the estate are crowded with the world's media. Satellite trucks line the verges.
Local people have come to look: some to express their horror, some out of simple curiosity. In the background, white-suited French forensic experts comb the scene, looking for clues to an extraordinarily brutal crime.
CCTV footage caught the van a few minutes later accelerating towards an open building which contained many jars of flammable liquid. Shortly afterwards, there was a blast.
The fire brigade was called and, at just before 10:00, one of the fire officers caught the suspect trying to open bottles of acetone at a second hangar, Mr Molins said.
The decapitated body of Mr Salhi's boss, the 54-year-old owner of a local transport company, was found nearby.
His head - reportedly bearing Arabic inscriptions - had been hooked on to some factory railings, alongside two flags also with Arabic writing on it.
Mr Molins said the suspect was a father of three who had been married for 10 years. His wife, sister and another person have also been taken into custody.
Mr Salhi, Mr Molins said, had never been found guilty of any crime but had been "under surveillance for radical Islamist activities since 2006".
Before her arrest, Mr Salhi's wife told Europe 1 radio of her shock at his arrest, saying he had left for his delivery job as normal and was due home for lunch.
"We have a normal family life," she said.
President Francois Hollande ordered security in the region to be tightened to the highest possible level for the next three days.
He said earlier: "We have no doubt that the attack was to blow up the building. It bears the hallmarks of a terrorist attack."
Speaking to reporters before flying back from an EU summit in Brussels, he reflected on the fact it would remind people of the attacks in and around Paris in January that killed 17 people.
"We all remember what happened before in our country. There is therefore a lot of emotion," he said.
US-owned Air Products makes gases and chemicals for a wide range of industries, including technology, energy, healthcare, food, and has employees in 50 countries around the world.
Chief Executive Seifi Ghasemi said: "I believe I speak for all of our Air Products family around the world in expressing our deepest sympathies to the family of the victim of this unspeakable act.
"My heart also goes out to the people who work at the site and their families."