The French rail operator SNCF is holding a 48-hour flash sale, with 500,000 tickets at just €19 for a one-way trip.
The sale is the latest attempt to tempt passengers back onto the railways after the epidemic decimated business.
After virtually no trains ran during the lockdown, SNCF has built back up to normal service, but has still seen a steep decline in customers, despite the summer holidays proving a temporary boost.
SNCF estimates that 16 million people travelled by train in France in July and August, down from a seasonal average of 25 million.
The sale has begun on the SNCF website and covers all tickets booked for journeys between September 8th and November 2nd on the budget Ouigo services, which cover 41 destinations in France.
The tickets follow normal SNCF booking rules, which means they can be cancelled or exchanged free of charge up to 1 hour 30 mins before the time of travel.
The sale lasts until the end of Thursday, September 3rd.
The power failure in south west France affected thousands of passengers who were travelling back to Paris and the north of the country ready to go back to work on Monday.
The power failure happened between Dax and Bordeaux on Sunday afternoon, leaving several trains from Dax, Biarritz and Hendaye stuck on the lines unable to move. Many passengers were stranded for up to 20 hours and some were forced to sleep on trains after local hotels ran out of space.
In all around 2,500 passengers were affected, said SNCF.
The company added that the problem is not yet resolved and has also had major knock-on effects on the rail network, saying that they do not expect a return to normal until Tuesday morning at the earliest.
Passengers who were booked to travel through the affected areas on Monday are advised to postpone their trip.