Officials of France's state-run railway company have vowed to remain vigilant following bomb threats, but say the network is back to normal.
A search last week failed to find explosives
A search last week failed to find any explosives, after a group known as AZF said it would detonate 10 devices if the government failed to pay a ransom.
But officials said the group remained a threat, amid criticism over the fact that the scare was made public.
Linguistic experts have been brought in to analyse letters the group wrote.
It sent notes to the presidency and the Interior Ministry demanding $4m and 1m euros (£2.5m in total).
Investigators have been examining the handwriting and language in the hope of getting clues as to the origins and further plans of the group.
Experts suggest the people behind it are not religious or political radicals, but more likely to have personal motives such as a desire for revenge.
There is also a theory that former members of the armed forces are involved.
Despite the continuing threat, the head of the state-run SNCF network, Louis Gallois, told French media that trains would be running normally.
"If we felt that our customers were at risk, we wouldn't run the trains," he said.
In February a bomb was discovered on a rail viaduct near Limoges
But the railway's executive vice-chairman Guillaume Pepy said SNCF continued to be on "heightened vigilance".
An unnamed senior judge told Liberation newspaper over the weekend that publicising the scare had driven the group underground and this meant they would continue to be dangerous.
"During the entire period when this affair was being kept secret the danger to the public was minimal, because negotiations were under way," the source said.
"Now that it has been made public and that contact has been broken, the threat is real."
The government has previously been criticised for keeping the threat secret.
This is the group's second such threat - in December a bomb was discovered on a track in central France after a blackmail letter was sent to the government.
In it, AZF said it was "a secular brotherhood with ethical and political connotations", according to the AFP news agency.
The group denounced "politicians more interested in themselves than the state", a "reductive education system" and an "economy that has lost its way".
A later note directed the police to a sophisticated explosive device laid on a viaduct near Limoges in central France on 21 February.
The BBC's Caroline Wyatt in Paris says the group appears to be named after a chemicals factory in southern France where an explosion in 2001 killed 30 people.