The guard was killed when the gang used explosives to blast their way into the Temis deposit centre, near Orly airport south of Paris, where armoured vans pick up cash, police said.
A source close to the matter said the dead man was in his 50s. Le Parisien newspaper said his legs were blown off by the blast.
Two other guards were wounded but their lives are not in danger, police official Pierre Dartout said. He could not say whether the thieves managed to take any money during the raid.
"We were targeted by a very violent armed raid," the head of Temis France, Gilles Goudron, said at the site of the robbery.
"This is organised crime, attacking the headquarters of a cash delivery company is taking things up a rung. Normally, armoured vans are attacked, not the building itself," police union spokesman Luc Poignant said.
Psychologists have been sent to the centre to help those affected.
The thieves struck before dawn, wearing black outfits and balaclavas. They used explosives twice to get into the centre.
"They had armbands and I thought they were police," a local cafe manager who gave his name as Lucien told AFP.
"I thought it looked dodgy and I went outside. One of them said to me 'get back inside or I'll shoot you.'"
Dartout said the attackers blocked the road with a burning car and a hijacked bus to ensure their escape.
The attackers fled in two vehicles, opening fire on police with Kalashnikov assault rifles, a police source said.
The thieves briefly took a male passer-by hostage in one of their cars. He was released unharmed in Vitry-sur-Seine, a few miles (kilometres) to the north.
"These are professionals and that proves their determination. They're ready to do anything for money, including killing people," said Noham Etissier of police union Alliance.