French police tweeted out a public appeal for help in hunting down the gunman. Members ofthe public are warned not to approach "the dangerous individual" but to alert authorities by contact the emergency number 197.
Around 720 police officers and other security forces are searching for him, Interior Minister Christophe Castaner said, and the public is being urged to alert police of any tips on his whereabouts.
The 29-year-old man sought by police over a shooting in Strasbourg lived in a small apartment in a ramshackle housing bloc and has convictions in France and several European countries after a life of crime, officials say.
The man, Cherif Chekatt, lived in the Poteries area of Strasbourg about a 20-minute tram ride west of the centre of the French city and its Christmas market where the attack struck.
Here is an English version of the Police appeal regarding the shooting suspect in Strasbourg, France. pic.twitter.com/0ELf3ctUin— BreakingNAgency (@BreakingNAgency) December 12, 2018
The suspected gunman has been sentenced 27 times, mostly in France where he was born, but also in Germany, Switzerland as well as Luxembourg which are easily reached from Strasbourg.
His crimes range from violence to robbery, but not terrorism.
Chekatt was added to a watchlist of possible extremists while in prison in France in 2015 after he "called for practising a radical form of religion," French deputy interior minister Laurent Nunez said on Wednesday.
He has since been monitored by France's domestic intelligence agency, the DGSI, which is occupied monitoring a large number of suspected extremists in France.