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French counter-terrorism police have shot and wounded an unarmed woman in a full veil after she threatened train passengers, Paris authorities say.

Officers opened fire eight times when the woman refused to comply with police orders, a source told the ´óÏó´«Ã½.

The alarm was raised by passengers on an RER suburban train in the 13th district in southern Paris.

The Paris prefect said police then intervened at the Bibliothèque François-Mitterrand train station.

The woman was reportedly heard shouting "Allahu Akbar," or "God is greatest".

"Police feared for their safety," the source added.

She is said to be critical but stable after being shot in the abdomen. She was reportedly operated on in hospital.

Paris police prefect Laurent Nuñez said the woman may be a 38-year-old who in 2021 threatened security forces protecting sensitive sites in France from terror attacks.

Mr Nuñez added that she was interned on mental health grounds after the incident.

The officers who shot her were wearing body cams, government spokesman Olivier Véran said.

Two investigations have been launched by the authorities. One is regarding the woman's actions, and the other to determine whether the use of a firearm by police was justified.

The incident comes amidst heightened tension in France linked to the Israel-Hamas war.

Earlier this month, a teacher was killed and two people seriously injured at a school in northern France by an attacker who reportedly shouted "Allahu Akbar".

In the wake of the incident, France raised its counter-terrorism security alert to its highest level.