French officials described the attacks as "criminal actions" and said they were investigating whether they were linked to the Olympic Games.
The disruptions as the world's eye was turning to Paris were expected to affect a quarter of a million people alone on Friday and endure through the weekend, and possibly longer, officials said.
Transport Minister Patrice Vergriete described people fleeing from the scene of fires and the discovery of incendiary devices.
"Everything indicates that these are criminal fires," he said on Friday.
The incidents paralysed several high-speed lines linking Paris to the rest of France and to neighbouring countries, Vergriete said, speaking on BFM television.
The attack occurred against a backdrop of global tensions and heightened security measures as the city prepared for the 2024 Olympic Games.
French officials denounced the vandalism that stranded thousands of rail passengers. (AP PHOTO)
Many travellers were planning to converge on the capital for the opening ceremony, and many holidaymakers were also in transit.
As Paris authorities geared up for a spectacular parade on and along the Seine River amid tightened security, three fires were reported near the tracks on the high-speed lines of Atlantique, Nord and Est.
The disruptions particularly affected Paris's major Montparnasse station.
Videos posted on social networks showed the hall of the station saturated with travellers.
The Paris police prefecture "concentrated its personnel in Parisian train stations" after the "massive attack" that paralysed the TGV high-speed network, Laurent Nunez, the Paris police chief, told France Info television.
All eyes were on the central message boards as most services to northern France, Belgium and the United Kingdom were delayed.
Travel to and from London beneath the English Channel, to neighbouring Belgium, and across the west, north, and east of France was affected by what the French national rail company SNCF called a series of co-ordinated overnight incidents.
The disruptions particularly affected Montparnasse station in Paris. (AP PHOTO)
Government officials denounced the acts, though they said there was no immediate sign of a direct link to the Olympics.
The Paris prosecutor's office has opened an investigation, being led by the National Jurisdiction for the Fight against Organised Crime.
Crimes involving "the deterioration of property that threaten the fundamental interests of the nation" can draw a potential 15-year sentence and fines of 225,000 euros ($A370,000).
"Degradation and attempted degradation by dangerous means in an organised group" can carry a 20-year sentence and fines of 150,000 euros.
French media reported a major fire on a busy western route.
Sports Minister Amelie Oudea-Castera said authorities were working to "evaluate the impact on travellers, athletes, and ensure the transport of all delegations to the competition sites" for the Olympics.
Speaking on BFM television, she said: "Playing against the Games is playing against France, against your own camp, against your country."
Passengers at St Pancras station in London were warned to expect delays on the Eurostar. (AP PHOTO)
She did not identify who was behind the vandalism.
Passengers at St Pancras station in London were warned to expect delays of about an hour to their Eurostar journeys.
Announcements in the departure hall at the international terminus informed travellers heading to Paris that there was a problem with overhead power supplies.
SNCF said it did not know when traffic would resume and feared that disruptions would continue "at least all weekend".
SNCF advised "all passengers to postpone their journey and not to go to the station," specifying in its press release that all tickets were exchangeable and refundable.
Valerie Pecresse, president of the regional council of the greater Paris region said "250,000 travellers will be affected today on all these lines".
Substitution plans were under way, but Pecresse advised travellers "not to go to stations".
The troubles comes before an opening ceremony on Friday in which 7000 Olympic athletes are due to sail down the Seine past iconic Parisian monuments such as Notre-Dame Cathedral, the Louvre Museum, and the Musee d'Orsay.