Although the motives for his attack are not clear, he was heard to shout "Allahu Akbar!" as he opened fire and had shown signs of radicalisation in jail. So are French prisons breeding grounds for terrorists?
Chekatt's shooting spree cost the lives of a fellow Muslim, Afghan refugee Kamal Naghchband, as well as a Thai tourist, a Polish immigrant, an Italian journalist and a 61-year-old former bankworker.
He himself was shot dead after a 48-hour manhunt.
A 37-year-old man has been charged with helping him acquire weapons, including the 19th-century revolver he used in the attack.
Six other people, including his parents and two of his brothers, who were detained after the shootings, were released at the weekend.
One of his brothers said Chérif had been "brainwashed", while his father, Abdelkrim, said his son had shown interest in the ideas of the Islamic State (IS) armed group, but that he had told him they were criminals.
The Chekatt family is well-known to police in the area and Chérif was a repeat offender who had served time in jails in France, Germany and Switzerland.
Most of the perpetrators of terror attacks in France have had criminal records, many of them becoming involved with jihadist ideas in prison.
From petty crime to terrorism
But Farhad Khosorokhvar, an academic who has been involved in deradicalisation programmes, is not convinced that Chérif Chekatt was one of them.
"We have those whom I call fake jihadists, that is who use the notion of jihad in order to legitimise the action and then become famous, worldwide famous," he told RFI.
"If this Chérif Chekatt had not shouted 'Allahu Akbar!', that would have been treated as a kind of tragic action of somebody who had become involved in a kind of shooting, like the school shooting in the United States or shooting indiscriminately due to a psychic crisis."
Chérif Chekatt was on France's terror watchlist, however.
Guards reported he'd stuck up a poster of the late al Qaida leader Osama bin Laden in his cell during one of his stays inside.
After his death, IS claimed him as one of its "soldiers", although that is what it does for virtually all such violent acts nowadays.
Secularism and Islam
But Khosorokhvar argues that Chekatt's killing spree was a gesture of anger and defiance, rather than a religious one.
He argues that laïcété - the French interpretation of secularism - means that the authorities tend to confuse a strict interpretation of Islam with terrorist tendencies.
"In French prisons to identify fundamentalism [as] radicalisation," he says. "They believe, wrongly, because empirically we have no proof of that, somebody who is a fundamentalist, who trespasses the norms of laïceté, is somebody who is radicalised, which is not true because most of those people who became radical and killed people and used violence did not go through fundamentalism."
This analysis can become a self-fulfilling prophesy, according to Khosorokhvar, pushing some to take to violence as a form of revolt.
"This has a kind of perverse effect. By pushing them towards that, at one moment some of them become radicalised."
Is deradicalisation working?
There are violent jihadists in French jails, however.
Journalist Marc Ezrati met some of them on a visit to Strasbourg prison, including a man of Chechen origin who had been caught just before launching an attack.
"He explained that he classified people as categories of animals," he told RFI's Philippe Lecaplain. "There were jackals, hyenas – the hyena was me, the journalist, the sheep was a police officer and, no need to spell it out, what do you do with a sheep? You cut its throat."
But Ezrati, who found many of the men he talked to intelligent and sometimes personally charming, is not convinced that France's present deradicalisation programme is the best way to tackle the problem.
"The principle of deradicalisation, putting them all together, I’m not sure that’s the best idea," he said. "In fact, I think the individual contact that I established with the prisoners associated with this phenomenon of radicalisation makes more sense."
But he warned, "It’s more complicated, you have to get yourself accepted by these people. You have to set aside all ill feeling and your fears."
In response to the Strasbourg attack, the mainstream-right Republicans party called for all radicalised prisoners to be placed in solitary confinement, along with other measures such as deportation of "foreigners inciting hatred".
Calls for dialogue with convicted terrorists, however, would not marry well with their law-and-order stance and have yet to win widespread support among the countries' politicians.
Radical groups recruiting in prison is not a new phenomenon or exclusive to France.
In the 1960s and 70s the Black Panthers, who were not Islamists but radical left-wingers, won many members among the US's sizeable black prisoner population and, going back to the 19th century, Russian revolutionaries described the jails as their unversities.
But there are specific conditions in France today, according to Khosorokhvar.
"French prisons are in very bad shape," he points out. "When it comes to the major maison d'arrêt, short-term prisons, you have too many people in each cell, overcrowding, understaffing and many other characteristics.
"But then we have, of course, the restrictive interpretation of laïceté. In many cases in the French prisons the relationship to religion, in particular concerning Islam, than in other European prisons."
Attempts to cut down on prison numbers, such as former justice minister Christiane Taubira's penal reform moves under the previous government, have so far fallen foul of political battles between right and left, however.
And, as for changing official French attitudes to secularism, that would seem to be a long way off.