Yannick Blanc, the Paris police chief, said in an interview in Le Monde newspaper: "We know that we are going to grant residency papers to several thousand."
A nationwide protest movement had sprung up over plans to expel thousands of illegal immigrant families with children in French schools. Politicians, media and sports stars were among tens of thousands to sign a petition pledging to "protect" them from deportation.
The children are from families that entered France illegally and would normally be expelled along with their parents, but campaigners say that most of them know no other country and that deportation would be inhumane.
Bowing to pressure last month, the interior minister, Nicolas Sarkozy, told prefects, state-appointed regional governors, to reconsider cases on the basis of new criteria, such as whether a child has "strong ties" to France.
French schools are obliged to take in children regardless of whether they are in the country legally.
Government supporters say that blanket regularisation of all pupils from "paperless" families will encourage illegal immigration.
The government believes that there are between 200,000 and 400,000 illegal immigrants in France and is planning 26,000 deportations this year.
The Education Without Borders Network (RESF), which has co-ordinated the protest campaign, says that between 50,000 and 100,000 children of illegal immigrant families are in the French school system.
RESF has repeatedly said it mistrusts the government's measures - saying its proposed amnesty would concern only a fraction of the families facing expulsion - and has pledged to keep up the pressure in the coming months.