Monday marked the fourth day of the strikes, which unions have vowed to continue until at least June 28 unless the government backs down on its reform plan for the debt-laden operator.
SNCF chief Guillaume Pepy told BFM television the action has so far caused losses of around 20 million euros per strike day, though the disruptions often spill into non-strike days.
Rail workers began their strikes on two out of every five working days last week to protest the government's planned overhaul of the operator.
Just one in five high-speed TGV trains were running Monday, and one in six on other mainline routes, while two-thirds of regional trains had been cancelled.
About 20 percent of the Eurostar trains in and out of London have also been cancelled.
Pepy noted "quite heavy participation" for the strike on Monday, "though there are more trains than last time", a reference to the stoppages last week.
"From what I can see, France has not been paralysed," Pepy said, "but clients are being heavily penalised."
Under the reform plan, new hires would be denied the jobs-for-life and early retirement guarantees enjoyed by current rail employees, and the SNCF would be transformed into a private company whose shares are owned by the state.
The government has insisted it won't back down, while unions claim to have broad public support, with more than 510,000 euros pledged to a fund set up to compensate lost wages for striking workers.
President Emmanuel Macron, who has not spoken on the conflict publicly since it started, plans to give an hour-long televised interview at midday on Thursday.
Macron will also address the strike during a two-hour primetime interview Sunday with BFM television and the investigative news website Mediapart
Parliament is scheduled to begin debating the government's overhaul on Monday, though Macron has said he will implement the changes by decree in order to move quickly ahead of the opening of French passenger rail traffic to competition starting in 2020.
Monday's strike is scheduled to end at 8:00 pm, before resuming for another two-day stoppage on Friday.