What is his background?
Kassim is a 29-year-old father-of-three who hails from Roanne, in the Loire region.
He once worked as a supervisor at a social centre, where according to Le Parisien newspaper he worked in a canteen and looked after children.
But he soon began to show leanings towards terrorism, most notably at first when he recorded a rap album in 2009 where one of the songs was called "Terrorist". The chorus repeated the phrase "I am a terrorist".
When he returned to France from a trip to Algeria in 2011, a distinct change was noted by those close to him, some of whom said that he became obsessed with the Koran, reported Le Dauphiné Libéré newspaper.
He stopped smoking, grew out his beard, and asked for a prayer room at his work place.
A year later, he moved with his wife and children to Egypt and is understood to have become a fully-fledged member of the Islamic State group Isis.
It remains unknown exactly where he is now, although it is understood to be either in Syria or Iraq.
What has he been linked to in France?
Kassim has been linked to the double murder of two police officers in Magnanville in June, as well as to the brutal slaying of the priest in Saint-Etienne du Rouvray, near Rouen in July.
He has also been linked to the 15-year-old boy arrested on Sunday on suspicion of plotting a knife attack on people in Paris.
He was connected to at least one of the women arrested last week over a car found abandoned a week ago near Notre Dame cathedral in Paris.
"Women, sisters have moved to attack. Where are the brothers?... She brandished a knife and she hit a policeman… Where are the men?" he said on social media, according to Le Monde, after one of the women stabbed a police officer during her arrest.
In all of these cases, his involvement is understood to have been remote.
How does he operate?
Kassim has regularly appeared in Isis propaganda videos calling for attacks on French targets.
He appeared in a video praising the attack in Nice that left almost 90 people dead after a truck ploughed into a crowd of Bastille Day revellers.
He is known to frequent the encrypted messaging app Telegram, which is how authorities found that he was connected to the recent attacks.
According to Europe 1, Kassim can operate in online groups of up to 300 people where he will encourage people to carry out hate crimes and attacks.
He is understood to give precise targets and ideas for how to carry out attacks on them, the paper added.