The waiter's colleagues called police after he was shot in the shoulder with a handgun in the Noisy-le-Grand suburb east of Paris on Friday night, the source said, AFP reported.
Attempts to revive the 28-year-old failed and he died at the scene.
The gunman, who a witness said lost his temper "as his sandwich wasn't prepared quickly enough", fled the scene.
Police said a murder investigation has been opened.
With the shooter still on the run Saturday, shocked residents gathered outside the pizza and sandwich eatery.
"He was killed for a sandwich?" one asked, unbelievingly.
"It is sad," said a 29-year-old woman. "It's a quiet restaurant, without any problems. It just opened a few months ago."
But others noted high crime levels in the area, notably drug-dealing and public drunkenness.