Nicolas Sarkozy told France-2 television on Tuesday that officials had received almost 30,000 applications from families seeking residency papers when a deadline for requests expired at the weekend.
This was some 10,000 more than had been expected, but despite the higher numbers, Sarkozy stuck to an earlier prediction that just 6,000 applications would be accepted.
Some expulsion orders had already been served, Sarkozy said, and many more were in the pipeline.
Sarkozy, the clear favourite to represent the right in next year's presidential elections, has faced fierce protests over moves to send whole families packing and has invested a lot of political capital in the crackdown on immigration.
Sarkozy, the son of a Hungarian immigrant, tightened residency rules after youths in poor suburbs - many of them home to immigrant families - went on the rampage last year in a wave of rioting that shocked France.
He said: "You saw what happened in the suburbs, one sees the difficulty of France's integration system. What's the reason for this? The reason is that our immigration policy has not been mastered.
"Just coming to France does not give you the right to stay in France."
Some 4.5million immigrants live in France, official data shows, and the interior ministry estimates that there are between 200,000 and 400,000 illegal immigrants in the country.
Sarkozy championed a new immigration law that makes it harder for foreigners to bring their families to France, but easier for those with special talents.
Bowing to public protest, he agreed late last year to give families with school-age children until the end of the academic year to get their papers in order. As the school year wrapped up, Sarkozy agreed to grant residency to those who could prove a strong link to France, giving them until Monday to apply.
It may take months to decide many cases, and immigrants' rights activists vow to renew efforts to protect children from deportation once the new school year gets under way.