About 500 people have been accommodated in gymnasiums but the rest, including unaccompanied children as young as 12, have been sleeping outside, NGOs say.
Candidates in the French presidential election have called for changes in migration policy.
Migration has been a key issue in the run-up to the poll on 23 April.
A spokesman for the centrist candidate, Emmanuel Macron, said an agreement with Britain that left the French acting "as its border guards" would have to be reviewed during Brexit negotiations.
