Some 800,000 passengers are estimated to be affected this weekend, a quarter of million on Friday, warned SNCF.
One in four Eurostar trains will be cancelled on Friday and over the weekend following arson attacks on the French railway network.
SNCF urged passengers to postpone their trips and stay away from train stations.
The attacks come as Paris prepares for its opening ceremony, with 7,500 athletes, 300,000 spectators and an audience of VIPs.
Gabriel Attal, France’s acting prime minister, said: “The consequences for the rail network are massive and serious,” adding: “Our intelligence services and law enforcement agencies are mobilised to find and punish the perpetrators of these criminal acts.”
Jean-Pierre Faranadou, the chief executive of SNCF, said that “the French are under attack” and that the plans of thousands who had hoped to come to Paris for the Games had been “ruined”.
“Today, it’s the major [holiday] departures that are under attack, it’s a part of France that is under attack, it’s the French who are under attack,” he told BFMTV.
“It was also, of course, the inauguration of the opening of the Olympic Games, with many French people going up to Paris to enjoy a day or three to share in the joy of the Olympic Games. All that is ruined. But we’re not going to give up.
“It’s going to be a big job to fix this, but we’ll get back on our feet and you can count on us.”
“It will certainly last the whole weekend … it’s a day of sadness today.”
He said the sites targeted had been “specifically chosen to cause the heaviest consequences”.
But Mr Attal advised against jumping to conclusions over who was behind the attacks.
“The investigation is starting, and I would urge everyone to exercise caution. What we know, what we can see, is that this operation was prepared, coordinated, that key points were targeted, which shows a kind of knowledge of the network in order to know where to strike”, he said.
Emmanuel Macron declined to comment.