The boy was part of a gang of teenagers in the western town of Nantes who had stolen two cars on Sunday.
The group drove one of the cars into a police road block, injuring seven officers.
After fleeing police, the 13-year-old jumped into the river at around 1am on Monday morning.
Police have been searching for him ever since but the public prosecutor confirmed on Monday that he had still not been found.
"These were extremely violent acts," said public prosecutor Brigitte Lamy, according to local newspaper Le Telegramme.
"From the moment they saw the road block, the driver of the stolen car increased his speed, screeching his tyres and and hitting the two police vehicles at high speed."
"One officer was thrown ten metres in the air," said a police union representative.
Five other children, one of them a girl, were involved in the incident.
All of them are under 16 years old and three of them already well known to police for previous charges involving stolen cars and driving without licences.