The six judges in charge of the investigation issued about 10 arrest warrants on 28 June, it emerged on Monday after they met some 2,000 civil plaintiffs in the case concerning the 13 November 2015 attacks, in which 130 people were killed and more than 400 wounded.
Jihadi brothers sought
Top of the list are Jean-Michel and Fabien Clain, also known as Abdulwahid and Omar or Abu Adam al Faransi.
Born in France to a mother from the Indian Ocean island of Réunion, the pair converted to Islam from Catholicism, became friends of Toulouse attacker Mohammed Merah, were jailed for trying to go to fight in Iraq but eventually managed to go to Syria to join IS there.
The judges believe they are still in Syria today.
The inquiry needs to be wrapped up by September 2019, participants at the meeting said, so as to have a case ready before the pre-trial custody of the sole surviving alleged attacker, Salah Abdeslam, has to end in May 2020.
Finance and weapons
The investigators say they have made progress on two questions - how the plot was financed and where the weapons used came from.
Some of the money was sent from Syria via the UK, they say, while more was raised by robberies carried out by two brothers, Khalid and Ibrahim el-Bakraoui, who died in the March 2016 Brussels suicide attacks.
The assault rifles used in the attacks are believed to have come from a major arms trafficker from Amsterdam, who is a "bête noire of the Dutch authorities", according to the reports.
The investigators are also looking into the people-smuggling network that enabled the attackers to come to Belgium and France posing as Syrian refugees.
Eleven people, including Abdeslam, have been charged so far.
French judges are expected to charge two other men, who have already been charged in Belgium over the Brussels attacks, soon.
They expect to take the inquiry to India and Pakistan in the next few months.
Senators call for action against Salafists
A French senators' report has accused the authorities of "culpable inaction" on terrorism and called for a crackdown on the Salafi school of Islam.
The report, published Tuesday, was charged with examining how to tackle the "terrorist threat after the fall of the Islamic State" and found "real shortcomings" in the way the question has been handled.
It claims that "Salafism and Muslim fundamentalism sustain the internal threat" and that a "lack of courage" in taking it on has meant that "certain individuals under surveillance have not been prevented from taking action".
Salafism should be declared an "enemy of the republic's values" and all possible legal measures should be employed against it, the report says.
It estimates that there are about 130 mosques and prayer halls, frequented by 40-60,000 people, that follow the school of thought in France.
The report's 63 proposals also cover intelligence gathering, prison organisation and international cooperation against terrorism.