One arrested man suspected to have rammed a car into the factory had been investigated over possible ties to Islamist radicals, officials said.
President Francois Hollande said the aim was to blow up the factory.
Officials say the decapitated person was a local businessman.
His head was found on a post at the gates to the Air Products gas factory in Saint-Quentin-Fallavier, some 40km (25 miles) from Lyon.
Mr Hollande said the decapitated body had "inscriptions" on it. The French interior minister said: "A flag with Arabic writing on it was found at the scene".