The accident occurred late on Saturday night in Pantin, a suburb in the north east of Paris.
CCTV footage showed that the victim wasn't watching where he was walking at the time he was knocked over, police sources told L'Express newspaper.
The 45-year-old pedestrian was pronounced dead soon after.
Instead of stopping the bus driver, whose vehicle had no passengers on board at the time, decided to speed off and cover his tracks.
"We have a witness who says he saw the driver stop 200 hundred metres down the road, got out of his bus and returned to take a look at the victim, then drove off," the police source told the paper.
It's understood that the driver then took the bus back to the depot where he tried to wash the blood off the bus.
The paper reported that the driver returned to the scene of the hit-and-run later, where he was taken into police custody.
He now faces charges of manslaughter and for hit and run crimes.
A spokesperson for Paris transport chiefs RATP offered condolences to the family, promising to take "full responsibility" if found responsible for the man's death.