Who is 4th French terror suspect Hayat Boumeddiene?

PARIS -- For French authorities, Hayat Boumeddiene may hold the key to figuring out if her late partner, supermarket shooter Amedy Coulibaly and the Kouachi brothers -- responsible for Wednesday's massacre at a satirical newspaper -- were part of a bigger terrorist cell in France.

It is not yet known whether the men coordinated their attacks with each other, but Boumeddiene and the wife of Cherif Kouachi are reported to have exchanged some 500 phone calls in 2014.

Boumeddiene, who is one of seven children, has no criminal record, but she has previously been questioned by police over her association with known Islamic radicals.

Among them: Convicted terrorist Djamel Beghal. Photos show Beghal with Boumeddiene and Coulibaly posing with weapons in a forested area of central France.

But neighbors at their Paris apartment building said the couple seemed normal.

"They weren't mean people; they said hello, goodbye, they would hold the door," a neighbor named Cyril said. "I bumped into them many times."

Said and Cherif Kouachi were also described as unremarkable by people in their communities. We met 24-year-old Fatmi, who told us that he knew Said from his mosque in Reims.

"He was pretty quiet, he didn't talk very much. I saw him from time to time with his family," Fatmi said. "On the outside, he seems like a good guy, someone who stayed out of trouble."

But his brother, Cherif, was well known to French authorities, imprisoned in 2005 for trying to join jihadis fighting against American troops in Iraq, raising questions about why authorities were not following him more closely.

Investigators are now racing to get a clearer picture of how these attacks were executed. But for the moment, there are more questions than answers.