Police are hunting for the girlfriend of one of the three gunmen who brought three days of terror to France, saying she may be "armed and dangerous".

Hayat Boumeddiene, a suspect in the murder of a Paris policewoman on Thursday, is on the run after her partner Amedy Coulibaly was killed when armed officers brought his kosher supermarket siege to a violent end.

The 26-year-old could hold the key to the ongoing terror investigation, as police admit they could be dealing with a larger extremist cell and al Qaeda threaten more attacks.

Boumeddiene is believed to have travelled to Syria via Turkey in recent days, and may not have been in France when the supermarket siege began.

Details are emerging of the young woman of Algerian descent and the links between Coulibaly, 32, and the Kouachi brothers, who were killed two days after murdering 12 people at the offices of satirical magazine Charlie Hebdo.

Boumeddiene and the wife of one of the brothers exchanged more than 500 phone calls in 2014, according to Paris prosecutor Francois Molins.

She reportedly started wearing a niqab in May 2009 after meeting Coulibaly and was sacked from her job as a cashier.

Later that year, they were married in a religious ceremony but were not wed under French law, which requires a civil ceremony.

According to French judicial documents, the couple travelled with Cherif Kouachi and his wife in 2010 to southern France to visit radical Islamist Djamel Beghal, who was under house arrest.

The pair posed for photos during the visit, taking selfies and a snap of Boumeddiene pointing a crossbow at the camera.

Interviewed that year by counter-terrorism officers over Coulibaly's involvement in an attempt to free Paris Metro bomber Smain Ait Ali Belkacem from jail, she was open about her fanatical views.

According to Le Nouvel Observateur, she refused to condemn al Qaeda attacks, preferring to criticise America's military interventions around the world and the Western media.

Police search

A police search of Coulibaly's residence in 2010 turned up a crossbow, 240 rounds of 7.62mm ammunition, films and photos of him during a trip to Malaysia, and letters seeking false official documents.

In a police interview that same year, Coulibaly identified Cherif Kouachi as a friend he had met in prison and said they saw each other frequently, according to a transcript of the interview obtained by the Journal du Dimanche newspaper.

According to the newspaper, he told the police that people he met in prison used the nickname "Dolly" for him.

He was employed as a temp worker at a Coca-Cola factory and reportedly met then-President Nicolas Sarkozy in 2009.

"I know a lot of criminals because I met heaps of them in detention," he is quoted as telling the police.

Michel Thooris, secretary-general of France's police union, said he did not believe the men behind the Paris attacks were "three people isolated in their little world."

"This could very well be a little cell," he said.

"There are probably more than three people," he added, given that Cherif Kouachi and Coulibaly had had contacts with other jihadist groups in the past.

French Prime Minister Manuel Valls, speaking in a TV interview late on Friday, also indicated authorities are bracing for the possibility of new attacks.

"We are facing a major challenge" and "very determined individuals," he said.

Hostages

Meanwhile, the names of four hostages who were killed during the supermarket siege have been released.

Yoav Hattab, Philippe Braham, Yohan Cohen and François-Michel Saada lost their lives at the hands of jihadist Amedy Coulibaly in Porte de Vincennes.

A group representing the Jewish communities of France described their deaths as "cold-blooded and merciless".

Reports in the French media have suggested that some of the hostages were killed before commandos raided the kosher store during the gunman's evening prayer.

Security will remain tight in Paris throughout tomorrow, as rallies take place in the capital.

France's Interior Minister Bernard Cazeneuve, said: "There will be sharp shooters on the roofs, and there will be inspection of drains in advance. There will also be 56 teams of bike riders who will escort high-profile heads of state during the event."

On Saturday, an estimated 700,000 people "marched" in cities across France to pay their respects to the 17 people killed during the three days of terror.