Mr Castaner is expected at the market at around 10h55.
Strasbourg mayor Roland Ries has confirmed that today is first day the market will be open after the fatal attacks on Tuesday night, which killed two people, left one person in a vegetative state, and injured 12 others.
Chekatt - who was Strasbourg-born, a fiché S, had a significant criminal record, and had been radicalised in prison - managed to escape in a taxi after the shooting, and had been on the run from police since the attack.
He was killed last night after police received a tip-off that he had been seen in the Neudorf area of the city, and was injured. A local man called police to report that someone matching Chekatt’s description was seen moving “from garden to garden”.
When patrols arrived near Rue Lazaret, Chekatt was seen, and began shooting at them; officers shot back and killed him.
In a tweet, Mr Castaner thanked the officers who had "given the best, when faced with the worst".
Fabrice Poli, Grand Est regional secretary of police union Alliance Police Nationale, said: “He was like a wounded animal; his intention was to die as a martyr, and to try to kill. We must appreciate the cold-blooded calm of these police officers.
“They have done extraordinary work. They are quite shocked, and are receiving psychological support.”
Mr Poli also thanked the public for their help in the investigation, with many people having reported sightings of Chekatt, and sending other tip-offs and information to the police.
He said: “The number of sightings were significant. There were an incredible number of credible witness calls.”
The official propaganda media of the so-called Islamic State, Amaq, has now claimed Chekatt as “one of its soldiers”, but police in France have said there is no evidence that the gunman was working as part of an organised network.
Mr Castaner said: “The investigation is not closed, but there is no indication that he was part of a network, or that he had any particular protection [from Islamic State] is this context.”
Paris prosecutor, Rémy Heitz, who has been leading the investigation into the incident, is to make a statement from the TGI court (tribunal de grande instance) in Strasbourg at 11h; the same time at which the Christmas Market will officially re-open.
Mr Ries, mayor of Strasbourg, said that the city now hopes to "go back to normal" after being freed from "the sword of Damocles" that had been hanging over its head since the attack.
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