In June this year, a court ordered the SNCF and the government to pay damages of 60,000 euros ($80,000, £43,000) for WWII deportations.
The families are intending to demand "compensation for the prejudice suffered as a result of (their relatives') deportation - in livestock wagons, in inhuman conditions, knowing full well that people risked being murdered," one of their lawyers explained.
The families plan to give the railway company two months to reply before taking the matter to an administrative court, the lawyer added.
However, French railways are appealing against the June verdict and argue that they had no choice during the war but to do as they were ordered or face being shot.