SNCF said on Friday that signal boxes had been damaged by fires in a “massive attack”, affecting lines that connect Paris to cities in the north, east and south west of the country.
The company said further disruptions would take place over the weekend.
Christophe Dubi, the Olympic Games executive director, told the BBC he had seen a “quick reaction” from organisers.
“The organisers, including authorities and SNCF, have to prepare for different scenarios,” he said.
“What I see here is a quick reaction and that gives me a lot of confidence.
“I have to feel for all those impacted by these delays, but I have confidence that organisers are really well prepared for any situation and this is definitely one.”
Prime Minister Gabriel Attal described it as “co-ordinated and prepared acts of sabotage”.
Eurostar, which has trains from London to Paris, is encouraging passengers not to travel after delays and cancellations.
“Paris 2024 has taken note of incidents affecting the Atlantic, North and East lines of the SNCF rail network,” read a statement from Games organisers.
“We are working closely with our partner, the rail operator SNCF, to assess the situation.”
The Paris prosecutor’s office has opened a criminal investigation into the incident.
Amelie Oudea-Castera, the country’s sports minister, said it was an attack on “the athletes’ Games”.
“These Games are for the athletes who have been dreaming of them for years, fighting for the holy grail of standing on the podium, and someone’s sabotaging that for them” she told French broadcaster BFMTV.