"A few children... Were among the injured," an SNCF spokesman said, without elaborating.
"The investigation should determine the number of people present on the train (and those who) were not authorised to be on it," he said.
The unprecedented crash yesterday near Strasbourg of one of France's flagship high-speed trains was "a huge shock", SNCF chief Guillaume Pepy told a news conference.
"So far the accident is inexplicable," he added.
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The train ended up partially submerged in a canal in the town of Eckwersheim. Today, its silver and black rear locomotive still lay in the canal under a bridge, with the next carriage straddling the bank and the water.
The 11 dead were among 49 technicians and railwaymen tasked with testing the next-generation TGV ("train a grande vitesse" or high-speed train), which was due to go into service next spring.
Chevrier said sabotage or an attack had not been ruled out, but were considered unlikely causes.
A senior official in the Alsace region yesterday blamed "excessive speed" for the disaster.
The train was running at around 350 kph (217 mph) when it derailed, a source close to the inquiry said yesterday.
The Strasbourg probe into "involuntary homicide and injury" has recovered the train's black box data storage units.
While there have been derailments of French TGV trains in the past, yesterday's was the first to claim lives.
Yesterday's accident happened with France on high alert following a string of deadly attacks in Paris late Friday.
However there were no signs that the train derailment was anything other than an accident during testing.
In August, a Moroccan man was overpowered by two young American servicemen after he opened fire with a Kalashnikov on board a TGV train between Amsterdam and Paris.