The children had been taking shelter from the storms after playing baseball outside, Spanish media reported.
"It seems that the roof shifted and brought down part of the wall," the spokeswoman said.
Authorities in France issued a red alert across nine regional departments for the first time on Saturday.
The winds have caused widespread disruption in both countries, with about 1.3 million homes experiencing power cuts in France, according to electricity grid operator ERDF.
Tens of thousands in Spain were also left without power as high voltage lines were brought down.
The weather wreaked havoc on the roads, with fallen trees hampering engineers struggling to restore power.
In Biarritz, train, bus and rail transportation were cancelled and many stores were shuttered up.
Michele Alliot-Marie, France's interior minister, said 715 additional staff had been sent to the Perpignan region to assist aid efforts.
French President Nicolas Sarkozy announced he would visit the region on Sunday.
Apart from the children in the Spanish sports hall, a 52-year-old woman died in Barcelona late on Friday night when she was crushed by a collapsed wall.
|French authorities issued a red alert across nine regional departments [AFP]
Another woman died in the northern Castilla-Leone region when a door, lifted by the winds, crashed into her.
In Galicia, in northwestern Spain, a civil guard sergeant was killed by a falling tree as he was directing traffic.
In the southeastern Spanish province of Alicante, a 51-year-old man was also killed by a collapsing wall, while one of six seamen rescued from their Portuguese cargo ship by helicopter off Galicia died, local media reported.
The death toll also included a municipal employee near Barcelona and a 60-year-old man in Spain's Catalonia province.
Four people died in southwestern France, including two drivers who were killed by falling trees in the Landes department.
A 78-year-old also died when he was hit by flying debris outside his home, local authorities said.
A 73-year-old women died in the southwestern Gironde department when the storm cut electricity powering her breathing machine.
In Spain's northern Basque country, waves as high as 21.5 metres were recorded off Cape Matxitxako.
Dozens of people had to be evacuated from the area after wind blew the roofs from their homes.
Some 14,000 people were also evacuated from the Alicante region due to a forest fire apparently touched off by a broken electricity cable.
Flights were disrupted across northern Spain from Bilbao in the Basque Country to Ibiza in the Balearic Islands, while rail travel was also disrupted.
Most ski stations in the Pyrenees mountains closed due to the risk of avalanches.
Air France cancelled domestic flights passing through the affected zone, and all rail traffic was halted in the Midi-Pyrenees region, mainly because of fallen trees on the tracks.
Authorities said Bordeaux airport and the Aquitaine bridge across the Gironde river were closed, and flights were also suspended at Toulouse airport.
SNCF, France's rail operator, said there would be no trains in the region before Sunday.