French President Emmanuel Macron has ordered police to take a "special approach" to radicalised young people after a teacher was stabbed to death in an apparent extremist attack.
Mr Macron wants police to comb through their files on people who could be deported from France to make sure nobody is overlooked, an Elysee Palace adviser said.
He has asked police to pay close attention to "young men between the ages of 16 to 25 from the Caucasus", the adviser said.
Police have named the suspect in Friday's killing as Mohammed Moguchkov, 20, who was born in Russia's predominantly Muslim republic of Ingushetia in the Caucasus.
French teacher Dominique Bernard, 57, was killed at the school in Arras, north-eastern France. It came almost three years to the day since the beheading of teacher Samuel Paty by Abdullah Anzorov, a radicalised Chechen.
Friday's stabbing has prompted calls for tighter security at schools and 7,000 troops have been mobilised.
In a statement on Monday, Mr Macron called Friday's stabbing a "tragic echo" of Mr Paty's killing in Conflans-Sainte-Honorine.
"In Arras as in Conflans-Sainte-Honorine, Islamist terrorism struck what it rightly regards as its greatest enemy: our school," Mr Macron said.
"The terrorists know there is no republic without the school, without patient learning in our classrooms of critical thinking and of the values of liberty, equality, fraternity and secularism that shape our citizens."
He said France would "continue to act so that our schools remain a sanctuary".
Schools were expected to hold a minute's silence on Monday.
The Elysee adviser said Mr Macron wanted ministers "to embody a ruthless state towards all those who harbour hate and terrorist ideologies".