Prime Minister Jean Castex, who rushed to the scene, said the main attacker had been arrested. A second person was also in custody.
“I was in my office. I heard screams in the road. I looked out of the window and saw a woman who was lying on the floor and had taken a whack in the face from what was possibly a machete,” a witness told Europe 1 radio.
Another neighbor, who heard the attack, told Reuters there was a long, deathly shout from “a person who was screaming and screaming.”
Castex said the two wounded were attacked at random when taking a cigarette break. The life of neither was in danger, he said.
“This attack happened in a symbolic place at the time when the trial of the terrible attacks on Charlie Hebdo took place,” he said.
Europe 1 radio quoted police officials as saying the main suspect was 18, was known to security services and was born in Pakistan.
One police source said a machete had been found at the scene. Another police sources said a meat cleaver had been found there.
The national antiterrorism prosecutor's office said it was investigating the case.
TRIAL UNDER WAY
Fourteen people went on trial in Paris on Sept. 2, accused of being accomplices in the attack on the Charlie Hebdo offices in January 2015 that killed 12 people.
Police moved Charlie Hebdo's head of Human Resources from her home this week after threats against her life.
On Friday, TV footage showed ambulances, fire trucks and police cordoning off the area around Charlie Hebdo's former offices.