The children have been identified and reported by families in France or in areas under Kurdish control since the collapse of the Islamic State (IS) group in 2017.
Only some of them have been identified and located in the Kurdish area, which will pave the way for their repatriation.
Children, mostly under the age of six, will only be able to leave with the consent of their mother, who will remain there, according to someone close to the story.
France excludes the return of any adults, combatants or wives, considered as activists of IS, much to the annoyance of lawyers representing families in France.
"Those who have committed crimes in Iraq and Syria must be tried in Iraq and Syria," according to a statement from the French foreign ministry.
"The exception is minors, whose situation will be examined on a case-by-case basis, and there is a particular duty to safeguard the best interests of the child,” the statement adds.
Repatriation, however, looks very complicated. Syrian Kurdistan is not a state recognized by the international community, and Paris does not maintain diplomatic relations with Damascus.
680 French IS fighters
In total, about 40 families, mothers and children, have been reported in Syria.
There is also a few "dozens" - 30 to 40 - French-speaking fighters would also be prisoners of the Syrian Kurds, adds the source quoted, without specifying if any French are among them.
In Iraq, only three families of French jihadists have been identified. One of the mothers, Mélina Boughedir, sentenced to life imprisonment, agreed to let three of her children go.
Of the 680 French jihadists estimated to be involved in the Iraqi-Syrian theater, more than 300 died and a small number joined other countries (Afghanistan, Maghreb, Libya), said Paris. Some of them are still there.