The storm caused widespread devastation across France and Spain
The authorities in south-western France and northern Spain have begun to repair houses, roads and power lines damaged by hurricane-force winds on Saturday.
At least 20 people were killed in various incidents as the fiercest storm in a decade blew in from the Atlantic.
Torrential rains and winds of up to 184km/h (114mph) were reported.
Earlier, the mayor of a Spanish town near Barcelona declared three days of mourning for four children killed when a sports hall's roof collapsed.
Between 20 and 30 youngsters were in the sports hall when it collapsed
"The entire population is shocked by this tragedy," said Jaume Bosch, the mayor of Sant Boi de Llobregat.
Mr Bosch said condolences had poured in from across the country, including from Spanish Prime Minister Jose Luis Rodriguez Zapatero.
The youngsters who died had gathered to play baseball on Saturday, but the fierce winds drove them to take shelter in a covered area for spectators.
Although an initial investigation has not yet been concluded, officials said it appeared that when the building's roof shifted, it brought down part of an adjoining concrete wall.
'Badly damaged'
As the storm moved over Italy and the central Mediterranean on Sunday, teams of technicians were deployed across France and Spain to help repair damaged power, telephone and rail networks.
"The priority today is to restore electricity as quickly as possible," said French President Nicolas Sarkozy as he visited a crisis response centre in Bordeaux.
A thousand workers from the French electricity grid operator, ERDF, are trying to restore power to around 800,000 homes that are still without power.
Technicians from across Europe have been sent to help repair power lines
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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