Yassin Salhi, 35, caused an explosion by ramming his vehicle into an area containing flammable liquids, prosecutors say.
His boss, the owner of a delivery firm, was found beheaded alongside flags with Arabic inscriptions.
President Francois Hollande has held a security meeting with ministers.
Prime Minister Manuel Valls cut short his visit to South America to return to France which is on its highest state of alert after the attack in the small town of Saint-Quentin-Fallavier some 40km (25 miles) from Lyon.
Officials and residents of Saint-Quentin-Fallavier gathered outside the town hall on Saturday morning to observe a minute's silence.
Mr Salhi was arrested at the Air Products factory on Friday morning.
Later, anti-terror police searched the apartment of Mr Salhi, a father-of-three, in the Moines neighbourhood of the town.
They took his wife and sister into custody. Another man was arrested but released without charge.
Agnes Thibault-Lecuivre, spokeswoman for the Paris prosecutor's office, has said police have so far not found any motive or possible foreign connection, and that Mr Salhi is not speaking to investigators.
Under French anti-terrorism laws, suspects can be held for up to four days before either being released or charged.
Yassin Salhi had been investigated in the past about his alleged links with Islamist militants.
It is alleged he was waved through the gates of the factory because he was a regular delivery driver.
Police and firefighters later found a half-destroyed car which had been rammed into canisters containing chemicals and a man trying to ignite more.
Mr Salhi's boss, a 54-year-old man whose name has not been released by police, was found beheaded at the scene.
His head had been placed on the factory railings. It is not clear when he died.
Speaking after the attack, President Hollande said: "We have no doubt that the attack was to blow up the building. It bears the hallmarks of a terrorist attack."
He said the attack 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 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."
A man suspected of carrying out an attack on a factory near Lyon in France in which a man was found decapitated continues to be questioned by police.