Four people were seriously injured when the man went on the rampage with a knife and an iron bar by the Canal d'Ourcq in northern Paris late on Sunday evening.
Two were British tourists in the 50s, another was an Egyptian tourist in his 40s and another a young local resident.
Three were still in hospital on Sunday evening, one of them in critical condition.
Police have not identified a terrorist motive and eyewitnesses say the man appeared to be on drugs.
But blood tests of the suspect, who was still in hospital on Tuesday, did not reveal any traces of drug use, a legal source told the AFP news agency.
His identity has yet to be confirmed, although papers on him said he was an Afghan born in 1987.
Interior Minister Gérard Collomb praised the "great reactivity and bravery shown by several citizens" in a statement.
The man was overcome by bystanders, some of whom threw balls used in the French bowls game pétanque at him.
An investigation into attempted murder has been opened.