Seven people have been injured after the attack including two English tourists.
A French police source said: "At this stage, there is nothing to indicate that it could be a terrorist attack".
The paper said the perpetrator stabbed three people near a cinema on the Bassin de la Villette, and men playing pétanque nearby attempted to stop the man, with one throwing a ball at him.
"Around four or five balls hit him in the head, but they weren't able to stop him", he added.
'He had an iron bar in his hand which he threw at the men chasing him, then he took out a knife, ' he told AFP.
US military conducts exercise in Syria amid growing US-Russian tensions
The base is used by USA special forces to train Syrian fighters who are confronting Islamic State militants. The United States does not seek to engage in battle with the Syrian government and those who supports him.
Police investigators work on the scene after seven people were wounded in knife attack downtown Paris, France, September 10, 2018.
There have been several knife attacks in France over the past few months, but few have resulted in terrorist investigations.
The motive for the violence remained unclear despite a claim by the Islamic State group that it was an attack by one of its fighters responding to the terror organisation's propaganda.
French police have arrested the knife-wielding attacker who injured seven people in the capital, four of them seriously.
The victims were all rushed to local hospitals, where their conditions were described as "serious but not life threatening".