France beheading
French crime scene investigators work next to a black plastic sheet outside a gas company site in Saint-Quentin-Fallavier, near Lyon where a decapitated head was found.Reuters

The wife of the key suspect in the attack on a French factory has described her shock on realising the terrorist is her husband.

Yassin Salhi, 35, was arrested after a man was decapitated and two people were hurt in explosions at the site.

A woman claiming to be the suspect's wife called French radio station Europe 1 in a state of distress and confusion having watched the scenes unfold on TV.

She said: "My sister-in-law called up and said switch the telly on and look at the news. She was crying. My heart stopped. I couldn't understand it.

"I do not know what has happened. Have they arrested him?"

She said her husband went to work as a delivery driver at 7am and that she expected him home in the afternoon.

"I've been waiting for him," she explained. "We are normal Muslims. It is Ramadan. We have three kids and a normal family life."

"Who can I call to give me more information because here I do not understand? I'm afraid to do anything."

French authorities have confirmed that four people have now been arrested in connection to the attack. A second suspect was arrested at his home in Saint-Quentin-Fallavier.

Yassin Sahli, his wife and his sister are being held in police stations near the scene.

"We are nearly certain that Yassin entered the [Air Products] plant alone, and that there is no second attacker," police sources told Le Monde.

The 50-year-old victim, who is the head of a company from the Rhône administrative region, is believed to be Salhi's boss. He has not been identified.

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After the attack, Salhi shouted "Allahu Akbar" (God is great) as he met the team of firefighters, who answered the emergency call.

The fire-fighters managed to overpower the 35-year-old before the gendarmes (France's paramilitary police officers) arrived.

Salhi was known to anti-terror police for radicalisation. A file had been opened on him in 2006 for radicalisation - meaning he should be watched - but it was not renewed in 2008 and authorities no longer deemed him a risk.

Salhi, who is from Saint-Priest, just outside of Lyon, does not have a criminal record.

The suspect had a 'link' to the Salafi movement, a group within Sunni Islam, but was not implicated in any terrorist activities.

It's the fourth terrorist attack in France in 2015.