The attack took place at 0900GMT in a commercial street in Romans-sur-Isere, officials say, adding alleged attacker was arrested.
A man wielding a knife attacked residents venturing out to shop in a town under lockdown south of the French city of Lyon on Saturday, killing two people and wounding others, prosecutors said.
The alleged attacker was arrested by police nearby. Prosecutors did not identify him.
They said he had no documents but claimed to be Sudanese and to have been born in 1987.
Prosecutors said that other people were also wounded but couldn’t confirm French media reports that there were seven other casualties, of whom one is in critical condition.
They also did not confirm reports that the man had shouted "Allahu akbar" (God is great) as he carried out the attack.
The office said it is evaluating whether the attack was motivated by terrorism, but that it has not launched any formal proceedings to treat it as such.
Like the rest of France, the town's residents are on coronavirus-linked lockdown.
The victims were carrying out their weekend food shopping on the street that has bakeries and grocers, the office said. Two-metre distancing is being encouraged as in the rest of the country.
Number of knife attacks
Media reported that the attacker first went into a tobacco shop and stabbed the tobacconist and two customers, before attacking several other people in the vicinity of that shop and a nearby bakery.
There have been a number of knife attacks in France in recent months.
In January, French police shot and injured a man in Metz who was waving a knife and shouting "Allahu akbar".
Two days earlier, another man was shot dead by police after he stabbed one person fatally and wounded two others in a Paris suburb.