The Briton, who rides for Team Sky, posted a picture on Twitter of his damaged bike and reported the incident to local police in southern France.
Commissioner Frederic Le Pollozec, of Menton police, said there had not been  significant progress in the inquiry.
"We couldn't find any other person to say anything about the crash," he said.
Froome, 32, is due to begin the defence of his Tour de France title on Saturday. He was not badly hurt in the incident which happened at Beausoleil, near his Monaco home, on 9 May.
Commissioner Le Pollozec said that Froome was unable to remember the car's registration number, or identify the vehicle from CCTV footage.
"We showed him some pictures from the cameras and he couldn't say which one was the vehicle," he said.
"There was a verbal fight between the driver and Mr Froome before the crash, but it is difficult to find the driver.
"We took some pieces of paint from the bicycle of Mr Froome but we couldn't find any evidence to match it with a vehicle.
"For now, the investigation is partially closed because we don't have any more details."
Police have been unable to trace a car driver accused of ramming into three-time Tour de France winner Chris Froome while on a training ride in May.