The source at Al-Jala hospital said the 49-year-old Frenchman had been hit by three bullets in an attack in the city's Abeida district.
The unidentified victim was an employee of a company carrying out extension work at the Benghazi Medical Centre.
The French embassy in Tripoli, contacted by AFP, said it preferred "not to comment for the moment".
Benghazi, cradle of the 2011 revolution that ousted veteran dictator Moamer Kadhafi, has seen near-daily attacks on security and other targets as the weak central government struggles to rein in former rebel brigades turned militias.