French police have stormed a Jewish supermarket and killed a gunman who had taken a number of women and children hostage, according to police officials.

According to Reuters, at least four hostages from the supermarket were killed in the shoot out that took place between police and the gunman. Four more hostages were critically wounded in the attack.

The man, believed to be Amedi Coulibaly, had links to the same al-Qaeda jihadi cell of the two brothers suspected of carrying out the attack on the offices of the satirical magazine Charlie Hebdo.

Coulibaly's alleged wife, Hayat Boumeddiene, has escaped from the grocery siege, a police union spokesman told CNN.

The pair were suspects in the fatal shooting of a female police officer in the Paris' Monrouge area yesterday.

Coulibaly was previously convicted of attempting to free a convicted terrorist, Smain Ali Belkacem, who was responsible for the 1995 attack on the Paris transport system which killed eight people and wounded 120.