A man is on the run after injuring two women with a hammer in Chalon-sur-Saône, in eastern France.
The women were allegedly assaulted, about 15 minutes apart, by a man just before midday on Friday.
Witnesses said the suspect shouted "Allahu Akbar" ("God is greatest" in Arabic) during the attacks.
French prosecutors say they are treating the incident as a possible terror attack, but did not rule out other motives.
The women's injuries are not life-threatening, and local media report that they have already been released from hospital.
Officials asked locals not to share information on social media about the location of police while the manhunt for the attacker was still under way.
Earlier on Friday a man was arrested at Châtelet metro station in Paris after reportedly attacking a soldier with a knife at 06:30 (04:30 GMT).
It was the latest in a string of assaults against French troops, who have been deployed across the country in response to recent terror attacks.
The soldier was not injured in the incident.