The SNCF said the derailment on Friday, which also left dozens injured, was caused by a connecting bar that had come loose at a rail switch at the station at Bretigny-sur-Orge, about 25 kilometres south of Paris.
The joint bar "broke away, it became detached and came out of its housing," said Pierre Izard, the SNCF's general manager for infrastructure.
It "lodged itself at the centre of the switch, prevented the normal progression of the train's wheels and seems to have caused the train's derailment," he said.
The company said the switch had been checked on July 4th and that it was immediately ordering checks of some 5,000 similar joints on its network.
"We have decided to check equipment of this nature on the entire network and are starting now," SNCF chief Guillaume Pepy said.
Transport Minister Frederic Cuvillier said human error was not to blame for the accident, praising the train's driver who he said "had absolutely extraordinary reflexes by sending the alert immediately", preventing a collision with an oncoming train.
But he said France's regional rail lines were out of date, after the SNCF focused much of its attention in recent years on high-speed TGV lines.
"We cannot be satisfied with rolling stock that is 30 years old," Cuvillier said, adding: "The situation is severe, with the deterioration in recent years of traditional lines because of a lack of resources."
A railway passenger association also denounced what it called "rust-bucket trains" and the practice of coupling different types of trains together, demanding proper inspections.
A minute of silence was held at noon Saturday on all French trains and in all stations for the victims of the accident, which took place as many were leaving for summer holidays ahead of the Bastille Day holiday on Sunday.
The local prefect's office said the dead were four men and two women, aged between 19 and 82.
A source close to the investigation told AFP the dead included a couple in their 80s from Bretigny, three men aged 19, 23, and 60, and a young woman whose exact age was not immediately clear.
Formal identifications of the bodies were underway, the source said.
In what officials described as a "catastrophe", the train came off the tracks and crashed into the station platform at 5:14 pm Friday, as it travelled at 137 kilometres per hour on its way from Paris to the west-central city of Limoges.
Four carriages of the train jumped the tracks, of which three overturned. One carriage smashed across a platform and came to rest on a parallel track; another lay half-way across the platform.
There were 385 passengers on the train.
Hundreds of passengers were in the station at the time and many have posted pictures of the scene on Twitter.
A huge yellow crane arrived at the station to remove the overturned carriages early on Saturday afternoon.
The prefect's office said nine people had also been seriously injured in the accident, including two who were in critical condition. Health officials said at least 50 people had been treated for injuries.
Rescuers worked throughout the night searching for victims potentially trapped in overturned carriages, but the prefect's office said no more were expected to be found.
Autopsies were to be conducted on the bodies of the dead on Saturday.
The SNCF, judicial authorities and France's BEA safety agency were each carrying out separate investigations of the accident.
Witnesses said the crash site resembled a war zone, with 57-year-old passenger Marc Cheutin saying he had to "step over a decapitated person" to exit the carriage he had been travelling in.
Officials meanwhile dismissed reports from police unions of a group of people pretending to be part of rescue efforts and attempting to steal from the victims, and of gangs throwing stones at emergency workers.
Cuvillier said he was unaware of any reports of victims being robbed. He said one person was arrested for trying to steal a mobile phone from a rescue worker, but that it was an "isolated incident".
The Red Cross and France's SAMU emergency medical service also denied seeing any thefts or facing any problems in carrying out their work.
The derailment was France's worst rail accident since 2008, when a train collided with a schoolbus, killing seven schoolchildren.