The SNCF is meeting with union leaders to try to reach an agreement to avert a strike during the summer Olympics which take place between 26 July and 11 August.
Train drivers are calling for bonus payments for working through the Olympic period when more than 15 million tourists are expected to gather in the city.
Drivers held a strike on Tuesday with just one in five commuter trains running on some lines because of the dispute.
"We thought the talks were dragging on a bit and wanted to provoke something," Fabien Villedieu of the SUD-Rail union told Agence France-Presse last week.
"We have a heavy workload with 4,500 additional trains in August, so a whole range of our colleagues won't be able to go on holiday," he added.
Staff employed in other public sector services, such as hospital workers, have also threatened to strike during the Olympics.
Paris' rubbish collectors last week won a pay rise as well as an Olympic bonus, subsequently retracting the threat of summer strikes.
Metro and bus operator RATP has already offered an average bonus of €1,000 to workers, and this can reach up to €2,500 for the most sought-after drivers.
France's interior ministry, meanwhile, has offered police officers bonuses of up to €1,900 to work during the Olympics.
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