Family situations will be reviewed case by case and residence permits will be granted to those whose children were born in France and who do not speak the language of their parents' country of origin, the interior ministry said on Tuesday.
A ministry spokesman said that "this is not a large-scale amnesty". He said that each case would be reviewed by a committee made up of government officials and immigrant support groups.
Nicolas Sarkozy, the interior minister, was to give details of the plan during a speech later on Tuesday to the senate, as it starts debate on a new immigration law adopted by the lower house National Assembly last month.
The ministry gave no estimate of the number of families to be granted residence rights, although activists said they would represent only a tiny fraction of the total number facing expulsion.
France's centre-right government has vowed to step up the deportation of illegal immigrants - who number 200,000 to 400,000 in the country - as part of a toughening of immigration policy backed by three-quarters of the public.
Sarkozy was to give details of the
plan in a speech to the senate
Families with children enrolled at school had been given the right to remain until the end of the school year on June 30 - at which point state officials were under instructions to arrest them and take them to the border.
To encourage families to leave, the interior ministry recently increased the relocation allowance paid to illegal immigrants, from 150 to 2,000 euros ($190 to $2,500) a person, plus 1,000 euros for each child under 18.
Reseau Education Sans Frontiers [Education Without Borders Network] (RESF), which is campaigning for all the children and families concerned to be given French residence permits, dismissed the announcement as a token gesture.
RESF - which had previously said some 10,000 children were at risk of deportation - now believes at least 50,000 families to be concerned, based on interior ministry figures, he said.
"As many as 100,000 children of illegal immigrants are enrolled in French schools, so this so-called humanitarian gesture will reach a mere one or two per cent"
Spokesman, Education Without Borders Network
Richard Moyon, an RESF spokesman, said: "As many as 100,000 children of illegal immigrants are enrolled in French schools, so this so-called humanitarian gesture will reach a mere one or two per cent."
Teachers, parents and activists in the RESF network say many of the children are well-integrated and thriving in the French school system, and that to deport them would go against the principles of the republic.
Since late April, more than 40,000 people have signed an RESF petition against what they denounce as a "childhunt" - pledging to "sponsor, protect and house" the children and their families, even it if means breaking the law.
Reseau Education Sans Frontiers [in French]