French President Nicolas Sarkozy congratulated the police involved on the success of their work so far.
Detectives are now looking into a link between the anarchist group and the German far left, which has already admitted having taken action against trains carrying nuclear waste.
The French interior ministry said that those arrested had been taken in three cities, including Paris, after an investigation that had lasted a month.
The suspects are being questioned about acts of sabotage on railway lines in France.
On Saturday, metal rods had been jammed against overhead power cables, which had resulted in chaos to the national train services, and then, on Sunday a high-speed train was stopped after concrete blocks had been put on the line.
