The attack took place at a testing time for President Emmanuel Macron, who is struggling to quell a month-long public revolt over high living costs that has spurred the worst public unrest in central Paris since the 1968 student riots.
The revelation that Chekatt was on a security watchlist will raise questions over possible intelligence failures, though some 26,000 individuals suspected of posing a security risk to France are on the "S File" list.
Of these, about 10,000 are believed to have been radicalised, sometimes in fundamentalist Salafist Muslim mosques, in jail or abroad.
Police had raided the suspect's home early on Tuesday in connection with a homicide investigation. Five people were detained and under interrogation as part of that investigation.
At the Europa Bridge, the main border crossing in the region used by commuters travelling in both directions, armed police inspected vehicles. Police were also checking pedestrians and trains arriving in Germany from Strasbourg.
"We don't know where the attacker is and we want to prevent him from entering Germany," a spokeswoman for the German border police Bundespolizei said.
French Justice Minister Nicole Belloubet said there was no need for the government to declare a state of emergency.
Secular France has for years grappled with how to respond to both homegrown jihadists and foreign militants following attacks in Paris, Nice, Marseille and beyond.