With about 35 percent of train drivers, signal operators and inspectors having declaring they will be on strike, the SNCF said that only one in five TGV high-speed and intercity trains would run and one in three Paris regional services on Sunday.
The hardest-hit regions will be Burgundy, Provence, Normandy and the central Limousin.
On international lines such as Eurostar and Thalys, three out of four trains will run.
Officials said they would issue predictions for Monday on Sunday evening.
Although the number of strikers was down, they warned that this was not necessarily a sign that the strike was flagging since it was on a weekend.
Rail workers are taking strike action for two out of every five days and the following strike will be on Friday 13 and Saturday 14 April.
Bill goes to parliament
The rail workers' strike could last into June and beyond, union leader Laurent Brun declared on Friday after talks with transport Minister Elisabeth Borne broke up.
"There was no negotiation," the CGT rail sector chief said.
Other union bosses were also furious at what they claimed was a lack of dialogue in talks on Thursday and Friday, accusing the government of failing to explain what it dislikes about workers' current employment status, which it plans to scrap for new recruits once its bill is passed.
Parliament will start debating the rail reform bill on Monday with 200 amendments tabled and should vote on it on 17 April.
Left-wingers have vowed to take up the rail workers' cause and fight against what they see as a threat of privatisation, although the government says it has no such plan.
The right-wing opposition supports the reform in principal but have pledged to defend branch lines from the threat of closure.
Air France was also hit by strike action on Saturday, cancelling 30 percent of its flights.
There will be more strikes at the airline on Tuesday and Wednesday.