The suspect stabbed customers in a checkout line at a supermarket in La Seyne-sur-Mer on Sunday morning, according to local reports.
The customer was taken to hospital a non life-threatening chest injury while the cashier suffered a minor eye injury.
Also, earlier, on 15 June in Munich, Germany, a woman died after being stabbed that she was stabbed by an unknown man.
Investigators say that the woman attacked first got her.
Sebastien, the customer, said she was "in a panic, afraid, didn't understand what was happening to her, and had no strength left".
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'We do not know yet if these facts are terrorists but they are in any case terrorising, because this man who had not asked anything was attacked at the cash desk of a supermarket'.
Police later searched her home to find any links to ISIS or other terror groups.
A sense of edginess has been with France since a murderous series of killings in 2015 in the name of the Islamic State group.
The woman, who carried a physical handicap card, would undergo a psychiatric assessment. The attack in La Seyne-sur-Mer has not been linked to terrorism so far and is now being investigated.
Last month a knifeman shouting "Islamic Phrases" killed one person and wounded four others during a Saturday night attack in central Paris.