A man in his 30s thought to be the person who carried out the attack was later arrested.
The suspected attacker entered the factory in Saint Quentin Fallavier, about 30km southeast of Lyon, and set off several small explosive devices, a source told AFP.
A decapitated body was found near the factory, another source said.
"According to the initial findings of the inquiry, one or several individuals on board a vehicle, drove into the factory. An explosion then took place," the source said.
"The decapitated body of a person was found near the factory but we do not yet know whether the body was transported to the place or not."
Al Jazeera's Paul Brennan said local witnesses and news reports in France said that the remains of the victim's body were put on display.
Brennan said that the man who was arrested was aged about 30 and was reportedly known to police.
The total number of casualties was not immediately reported. It is not yet known what the text on the Islamic flag said.
The target of the attack is a chemical factory which is reportedly linked to a French company called Air Products that works with Total and specialises in liquid gas.
The attack occurred around 10am local time (08:00 GMT), according to local media.
The attack came nearly six months after the attacks in and around Paris that killed 17 people in January that started with a shooting at satirical magazine Charlie Hebdo.
French President Francois Hollande was to return home early from an EU summit after the attack, officials said.
"He will return early this afternoon and is in constant contact with Interior Minister Bernard Cazeneuve and the security services," the official said, adding that he would make a statement to the press in Brussels before 11:00 GMT.
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| Map Saint-Quentin-Fallavier [Al Jazeera] |