The 26-year-old widow of a gunman believed responsible for the deaths of four people is now the focus of an intense manhunt by French police.

Hayat Boumeddiene is the subject of a search by authorities, who believe she may have vital information relating to attacks in Paris this week that left more than a dozen people dead.

A Turkish official told the Associated Press that Boumeddiene may have fled France to Turkey, and crossed the border into Syria.

The Frenchwoman of North African origin is the common-law wife of Amedy Coulibaly, 32, who was killed on Friday when police stormed a kosher market in eastern Paris, where he had taken hostages.

Coulibaly is alleged to have killed four people before police brought an end to the ordeal.

Two days earlier, Said and Cherif Kouachi allegedly killed 12 people at the offices of the Charlie Hebdo newspaper. On Friday, the brothers were killed in a shootout with police.

French authorities now believe that Boumeddiene may have key information about how the attackers in both incidents were linked.

"Since 2010, she has had a relationship with an individual whose ideology has been expressed in violence, and by the execution of poor people who were just doing their shopping in a supermarket," Christophe Crepin, spokesman for the UNSA police union, told the AP.

Boumeddiene and a female companion of one of the Kouachi brothers exchanged some 500 phone calls, Paris public prosecutor Francois Molins told AP on Friday.

"We must interrogate her so she explains exactly if she did this under influence, if she did it by ideology, if she did it to aid and abet," Crepin said.

Boumeddiene and Coulibaly were wed in July 2009. Their religious Islamic ceremony was not recognized by French law.

Boumeddiene, who has never been convicted of a crime, has been pictured wielding a crossbow in photos and has accused the U.S. of killing innocent Muslims.

Interrogated by police

Boumeddiene characterized herself as an observant Muslim in a 2010 interview with French counterrorism police. But she referred to her husband as "not very religious" and someone who "likes to have a good time."

Court documents show that Boumeddiene was once asked by French counterrorism police about her thoughts on attacks carried out by al Qaeda.

"I don't have any opinion," she answered, but added that innocent people were being killed by the Americans and needed to be defended.

That same year, Boumeddiene decided to start wearing a full-length Islamic veil, which she told police led to her losing her job.

According to judicial records, French internal security services said that Boumeddiene had close ties to Islamic radicals.

A Turkish intelligence official told the AP on Saturday that authorities believe Boumeddiene may have fled France. The official said she may have arrived in Turkey days before the attacks in Paris and crossed the border into Syria.

The official said a woman by the name of Boumeddiene, and who matched descriptions of her appearance, flew to Istanbul on Jan 2. only to disappear after travelling to the Turkish city of Sanliurfa two days later.