Both victims were taken to hospital.
The 24-year-old assailant was overpowered by a customer and two supermarket employees and was taken into custody. Police later searched her home to determine if she had any links to the Islamic State group.
France has been on high alert following a string of jihadist attacks since early 2015, often by people who have become radicalised or claim to have acted in the name of the Islamic State group.