Five hundred back-up generators were being installed in affected towns and villages as an emergency measure, ERDF said. Twelve helicopters are also flying over the area to help build a detailed picture of the damage.
Technicians from Germany, the UK and Portugal have also been sent to help.
"After the storm, the electricity network is badly damaged... Access to the network is particularly difficult, complicating the work of our teams," ERDF said.
The French state rail operator, SNCF, also has 1,000 engineers and workers on the ground, trying to remove fallen trees and fix overhead electric cables.
The Paris-Toulouse high-speed line was still out of service, as well as a number of regional and local lines, SNCF said in a statement.
"More than 400 level crossings are out of order for lack of power supply, so it is not possible to give precise forecasts of when traffic can be restored. We advise travellers to postpone their trips on these lines," the company said.
Those stranded by the storm are instead being transported by coach.
Major roads across south-west France have re-opened, but not rail lines
Forestry officials meanwhile reported that huge areas of trees had been flattened by the storm in the Gironde and Landes departments.
Meanwhile in Spain, the electricity network operator, Red Electrica de Espana (REE), said the winds had disrupted supply on 17 lines in the north of the country. Tens of thousands of people in Galicia and Catalonia are without power.
Those Spanish airports that were affected have all re-opened, while trains are running normally except those crossing the French border.
The Spanish army meanwhile said it was supporting emergency services fighting a forest fire in Alicante, north of the resort of Benidorm, which started when gales felled an electricity pylon.
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