In general, children take their residency status from their parents, so when British parents apply for residency they will be asked about dependent children and the children are included on their parents' carte de séjour. The first one is where the children were born. If your children were born in France, you can apply on their behalf for French citizenship. If the parents gain French nationality, the child is automatically given citizenship so this may be a simpler way to do it. In terms of residency requirements five years is needed for both children and adults, so actually being born in France doesn't give children much of a head start.

Source: The Local October 09, 2019 12:45 UTC