The coordinated attacks were staged at 4am local time (0200 GMT).
At each site, the perpetrators targeted fibre optic cables that carry safety information for drivers and control rail changes, SNCF chief executive Jean-Pierre Farandou said.
Gerard Due, mayor of Croisilles in northern France, one of the sites hit, said the attackers had specialised equipment to access the cables and then “threw a flammable liquid” on them.
Vergriete said that the saboteurs had been spotted with “vans”, while “incendiary devices were found at the scene”.
Paris prosecutors opened an investigation into attacks on “the fundamental interests of the nation” and criminal conspiracy.
A similar sabotage attack was staged in Germany last year and in eastern France in January 2023.
The attacks left passengers stranded in stations across Paris and in many cities in eastern, western and northern France.
Some at Montparnasse station in Paris were left in tears.
Charles Fazio, a 70-year-old American from Florida, went to the station to try to get information. “I don’t understand anything,” he said. “We have to go to Lille tomorrow for the Olympics”.
French security forces are on their highest alert to prevent attacks during the Paris Olympics.
Workers carrying out maintenance at Vergigny, southeast of Paris, stopped one attempted attack there.
French officials refused to comment on the identity of the saboteurs.
Far-left French anarchists have a history of targeting the train network with arson attacks. The arson method used resembled past attacks by extreme-left activists, a security source told AFP.
President Emmanuel Macron has said in the past that Russia was planning to target the Games. Police arrested a Russian man this week in Paris who was suspected of “organising events likely to lead to destabilisation during the Olympic Games”.
