In a statement released on Friday evening, SNCF said traffic on the affected lines would “recover” on Saturday thanks to the work of thousands of railway workers.
It said:
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On the Eastern Line, trains will run as normal from 06:00 am (05:00 BST) on Saturday
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80% of trains on the Northern Line will be delayed by 1-2 hours
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60% trains on the South-Western line will be delayed by 1-2 hours
The company said customers whose trains are delayed or cancelled will be contacted via email or text message.
Eurostar said it expected around a fifth of services to be cancelled over the weekend, while all trains would face delays of around 1.5 hours. Eurostar services use the Northern High-Speed Line.
SNCF said monitoring of the rail network had been strengthened “on the ground and in the air” using 1,000 workers and 50 drones.
Junior transport minister Patrice Vergriete said about 250,000 people were affected on Friday, while up to 800,000 could face delays or cancellations by Monday.
He said the most likely motive for the saboteurs was to disrupt travel during the holiday season, rather than Friday’s Olympic opening ceremony.
“This has nothing to do with the Olympics,” he said in an interview.
The last weekend in July is traditionally a busy day for travel during the holidays.
No group has so far claimed it was behind the attacks. A source close to the investigation told AFP news agency the operation was “well-prepared” and organised by “the same structure”.
Mr Attal said security forces were searching for those responsible.
Government officials reported that at around 04:00 on Friday, saboteurs cut and set fire to special fibre optic cables needed for the safe operation of the rail network.
One site was in Courtelain, 150 km (93 miles) southwest of Paris. A photo posted online reportedly showed burnt cables in a shallow ditch and its protective SNCF paving stones thrown away.
The SNCF spoke of “massive heavy strikes” aimed at disrupting its services, not just at Courtalaina but also at Pagny-sur-Moselle, a village outside the eastern city of Metz and Croisilles, not far from the northern city of Arras.
Another attempted attack in Verginny, southeast of Paris, was foiled by SNCF workers who were carrying out maintenance work at the site on Friday morning.
Prosecutors have opened investigations into attacks on “the fundamental interests of the nation”.