The decision is motivated by the fact that knife attacks have become "very common", says Borne.
The searches will begin in the spring and will be carried out by the police, as school staff do not have the right to search students.
In early February, a 17-year-old student was seriously injured after a knife attack at his school in Bagneux, southwest of Paris.
In an area north of the capital, where crime rates are above average, around 20 upper secondary and high schools have been placed under police surveillance. According to the authorities, it is to "prevent a repetition of violent acts" after a series of incidents in Paris.