The local prosecutor's office said witnesses of the attack in a public park of the town center heard the attacker shout "Allahu Akbar" while hitting the women, who were taken to hospital but whose life is not in danger.
Prosecutors said they were treating the incident as a possible terror attack, but also did not rule out the possibility the attacker was deranged.
The attacker was still on the run on Friday afternoon, police said.
Earlier on Friday, 18 people were hospitalized on Friday after witnesses reported there had been a blast on a packed rush-hour commuter train in London and police said they were treating it as a terrorism incident.
Passengers on board a train heading into the capital fled as fire engulfed a carriage at Parsons Green underground station in West London at 8.20am (07:20 GMT), with some suffering burns and other injuries in a stampede to escape, witnesses said.
The London ambulance service said it had taken 18 people to hospital, but said none were thought to be in a serious condition.
In June, a man who was already on the radar of French authorities was killed after ramming a car carrying explosives into a police vehicle in the capital's Champs-Elysees shopping district, prompting a fiery blast.
No police officers or passers-by were hurt in the June attack. It is yet unclear why the attacker drove into police, though officials said the incident was apparently deliberate.