Police and hospital sources said the shooting of Laurent Barbot, 41, occurred at around 22.00 GMT as the victim - a resident of the kingdom - was in his car near a late night supermarket.
They said Barbot, identified as a technician who worked for French defence electonics company Thales, was dead on arrival with two gunshot wounds, one to the chest.
A Saudi security official told Reuters suspected insurgents loyal to al-Qaida might be behind the shooting - the first such fatal attack on Westerners in the cosmopolitan Red Sea city of Jeddah which has been relatively immune to al-Qaida attacks.
"There is a strong possibility that this is a terrorist attack", said a security spokesman at the Interior Ministry Brigadier-General Mansur Turki.
The Frenchman was the latest Westerner with defence links to be killed in Saudi Arabia. Three Americans working for US defence contractors were killed in Riyadh in June and earlier this month a British man working for electronics company Marconi was shot dead in the Saudi capital.
An al-Qaida statement claiming responsibility for the attack said the "crusader" company was providing services to Saudi Arabia's National Guard.
Many foreigners have recently
been killed in Saudi Arabia
The French Foreign Ministry confirmed the killing of Barbot and said it was in close contact with the Saudi authorities to determine the circumstances of his killing.
"A French national resident in Jeddah was attacked during the night. He died. An investigation is being carried out by the Saudi authorities with whom we are in close contact to determine the circumstances of this affair," a spokesman said.
Thales managing director Jean-Paul Perrier expressed shock but said the company would maintain its work and its 250 expatriate employees in Saudi Arabia despite Barbot's killing.
Saudi Arabia's rulers believe they have broken the back of an al-Qaida insurgency by waging a security crackdown recently, killing and arresting operatives after 17 months of bombings and bloody clashes.
But analysts say renewed shooting of Westerners this month shows that operatives, weakened by the crackdown which eliminated many of their top leaders, weapons supplies and infrastructure, can still strike their favoured targets.