Summary of events

- Three terror suspects are dead after a dramatic situation unfolded today in France, with police storming a printing plant and a Jewish market in Paris.

- French authorities had zeroed in on the two main suspects in the Charlie Hebdo terror attack. Brothers Cherif and Said Kouachi were holed up in a printing house in Dammartin-en-Goele, a small industrial town 25 miles outside Paris, and were holding a hostage. 

- After an hours-long standoff, the suspects emerged and opened fire. Explosions and gunfire could be heard as police stormed the location, killing the brothers. The hostage was freed.

- A separate hostage situation had also unfolded at a Paris grocery store, with 15-20 people held captive. The murder of a Paris policewoman Thursday has also been linked to that hostage-taker. He reportedly threatened to execute hostages if police moved in on the Kouachi brothers.

- At least four hostages died at the Jewish market and the hostage-taker was killed by police. Watch above the moment that authorities stormed the market.

Follow the continuing updates below.

Fox News chief intelligence correspondent Catherine Herridge brought us the latest this morning on the suspects.

She urged caution on a report that ISIS has claimed responsibility for the Hebdo massacre. As of yesterday, she said there was no credible claim of responsibility.

Herridge pointed to tweets from an account with known terror associations that had images of the Hebdo attack, combined with images of Anwar al-Awlaki and another American jihadist.

She said the messages Wednesday appeared to show foreknowledge of the attack, according to her sources.

Herridge said it's clear that both brothers had ties to al Qaeda affiliates, one in Yemen and the other in Iraq.

Right now, she said a lot of "dots" in the investigation point to al Qaeda in the Arabian Peninsula, the Yemen affiliate. 

A Reuters report said the older brother, Said Kouachi, trained in Yemen and is believed to have met with Awlaki, who was killed in a U.S. drone strike in 2011.

Watch her full report below.

UPDATE 8:05a ET: Greg Palkot reports that the second hostage situation - at a Kosher deli/grocery in eastern Paris - started when a gunman with two AK-47s stormed the location. 

It's believed there are women and children among the hostages in Porte de Vincennes.

Police believe the gunman is the same person who shot a Paris policewoman on Thursday.

According to a report, Palkot said the gunman admitted to randomly shooting the officer, who at the time was handling a traffic accident. 

He said reports now point to links between the two situations. Palkot said police reportedly found the DNA of the Hebdo attack suspects in the apartment of the man suspected in the policewoman's murder.

UPDATE 8:35a ET: Photos have now been released of two more suspects, including the man suspected of the grocery hostage-taking.

The woman on the left is said to be his girlfriend and acting as his accomplice.

Two people are reportedly dead at that location.

UPDATE 9:25a ET: A French official tells AP that the grocery store gunman yelled "you know who I am" as he opened fire.

More from AP:

Helmeted SWAT squads converged on the standoff. The French president ordered the country's top security official to the scene, an official in the presidency told The Associated Press.

The two men suspected in Wednesday's attack on satirical newspaper Charlie Hebdo have been on the run since gunning down 12 people and remain cornered by police about 30 kilometers (18 miles) away.

France has been high alert for other attacks since the newspaper massacre.

A French official said earlier that the two Hebdo suspects holed up at the print shop indicated they want to "die as martyrs."

UPDATE 9:35a ET: Fox News terrorism analyst and author Walid Phares weighed in on "America's Newsroom," saying if the Hebdo attackers really wanted to "die as martyrs" they would have done so on Wednesday outside the Charlie Hebdo office.

He said their actions in the past few days indicated the terrorists "wanted more." 

"They are buying time. My question is: why are they buying time? They could have engaged earlier. They are not," he said. 

Phares speculates that the attackers are giving outside terror groups a chance to produce the narrative that "two brave jihadists were fighting against an army of 1,200 French soldiers."

He said with each hour that goes by, the terror group that is responsible will view the operation as even more of a success.

UPDATE 10a ET: Greg Palkot reports that police allowed an elementary school near the printing house to be cleared of students. 

Amy Kellogg, also on the scene in Paris, said reports of two dead at the grocery store are not confirmed and the situation remains "fluid."

More details from on the hostage-taking involving the Kouachi brothers.

Officials told Fox News that there were four people inside the business when the gunmen went inside, but three people were somehow able to leave the area.

The Associated Press reported that at least three helicopters were seen hovering above the town. At nearby Charles de Gaulle airport, two runways were briefly closed to arrivals to avoid interfering in the standoff, but were later reopened. Schools went into lockdown.

Earlier Friday, a French security official told the AP that shots were fired as the suspects stole a car in the town of Montagny Sainte Felicite in the early morning hours. French officials told Fox News that the suspects threw the car's driver out at the side of the road. The driver, who recognized the suspects, then called police and alerted them to the suspects' whereabouts.

UPDATE 10:15a ET: Yemeni officials confirmed to AP today that Said Kouachi is suspected of having fought in Yemen for al Qaeda.

Another senior security official says Kouachi was in Yemen until 2012.

Both officials spoke to The Associated Press on condition of anonymity because of an ongoing investigation into Kouachi's stay in Yemen.

Kouachi is suspected of joining the militants at the time when Yemen's al-Qaida branch overran entire parts of the south amid the turmoil that engulfed the country during its Arab Spring uprising.

Many foreign students studying Arabic in Yemen were suspected of linking up with militants and were later deported. One of the officials says Kouachi was likely among a group of foreigners deported from Yemen in 2012.

UPDATE 10:30a ET: Paris police tell AP that the grocery store gunman threatened to kill hostages if authorities move in on the Kouachi brothers, who are holed up in a printing house outside Paris.

The Kouachi brothers are the main suspects in Wednesday's attack on Charlie Hebdo.

UPDATE 10:55a ET: An operation appears to be underway at the location where the Kouachi brothers are believed to be holding a hostage. 

Explosions and gunfire could be heard near the location, with smoke rising from the building. 

Watch the Sky News footage of the moments when police moved in. 

UPDATE 11:15a ET: Sky News' reporter on the scene reports explosions and gunfire coming from the grocery store.

She said police are moving reporters far away from the Jewish market and scrambling cell phone signals. 

UPDATE 11:20a ET: Sky News reporter says Kouachi brothers have been killed, according to wire reports, and their hostage is free. 

Several hostages have been freed from the market, Sky News reports, following explosions at the location.

UPDATE 11:35a ET: The hostage-taker at the Paris market has also been killed, Palkot reported.

He said he's waiting to confirm reports that all five hostages at the market were freed.

It's unclear what has happened to the female accomplice.

UPDATE 11:50a ET: Below is a photo of freed hostages with Paris police officers. 

UPDATE 12p ET: At least four hostages were killed in the Paris market, Reuters reports. 

Amy Kellogg reported earlier that there may have been casualties among police officers.

Greg Palkot said it appears there were 15-20 hostages being held in the market. He said police believed earlier in the day that there were only five or six hostages.

UPDATE 12:05p ET: AP reports that the assault on the Kouachi brothers at a printing plant began after the terrorists emerged from the building and opened fire.

UPDATE 12:20p ET: Shepard Smith just aired some riveting video from Sky News, showing the moment when authorities moved in on the Jewish market.

UPDATE 12:35p ET: Catherine Herridge has previously reported that Said Kouachi had ties to al Qaeda in Yemen, including traveling to the country. 

But she said it still remains unclear whether the Hebdo attack was directed by the foreign terrorist organization. 

Herridge said officials are focusing on a "gap" in the known whereabouts of Said. They know he was in Yemen in 2011, but after he went back to France, he and his brother were off the radar. 

She said one possibility is the brothers "went dark" after being given a mission, but another possibility is that they traveled to Syria to train with al Qaeda operatives there.

Stay tuned for more reporting from Catherine Herridge throughout the day on Fox News.

UPDATE 12:50p ET: In addition to the four hostages who died, Shep reported there were two police officers injured and four more hostages are in critical condition.

The female accomplice, who is believed to have acted as a getaway driver in the murder of a female police officer Thursday, remains on the loose.

UPDATE 2:10p ET: Catherine Herridge reported moments ago on more information that links the Kouachi brothers to al Qaeda in Yemen.

Herridge said the AFP report states that the gunman told the French TV station that the operation was financed by al Qaeda in Yemen, specifically Anwar al-Awlaki. 

She called the new information very important because it leads "overwhelmingly" to the attack being directed by a foreign terror group. 

UPDATE 2:30p ET: President Barack Obama spoke moments ago about the ongoing situation in France. 

The president said that he has spoken with his counter-terrorism advisor and that he has been in contact with the French government. 

"We're hopeful that the immediate threat is now resolved thanks to the courage and professionalism by the French personnel on the ground," Obama said. "But the French government continues to face the threat of terrorism  and has to remain vigilant.  The situation is fluid."

Watch the video below to hear more of the president's remarks. 

UPDATE 3:55p (ET): The Associated Press reports that a member of al Qaeda's branch in Yemen says the group directed the attack on the French magazine.