Separately, gunmen in Benghazi also shot and wounded an Egyptian who had been working in a grocery, while a Libyan police officer survived an assassination attempt, a security source said.
The Frenchman worked for a company upgrading a large hospital in Benghazi, which has been rocked by car bombs and assassinations amid Islamist militant activity, the official said.
"He was killed with three shots," the official said.
The French foreign ministry had no immediate comment.
The killing comes a week after police found seven Egyptian Christians shot dead execution-style on a beach outside Benghazi, home to several oil firms.
No one has claimed responsibility for the killing of the Egyptians but residents said gunmen had looked for Christians in their neighborhood, suggesting radical Islamists might be behind it.