The fate of the children, ranging in age from 6 months to 8 years old, is in legal limbo. Their father's whereabouts are unknown.
The woman's lawyer says the family should be brought to France. But French government spokesman Christophe Castaner said today that the mother should be prosecuted in Iraq, saying she wasn't in Mosul "for tourism."
France estimates that 750 French people are among extremists in Iraq and Syria, including up to 450 children.