When you’re ending a marriage or a civil partnership, parental authority is retained jointly by both parents. Who exercises that parental authority has no particular consequence on the rules. Nonetheless, in France the judge may decide to entrust the exercise of parental authority to just one of the parents if this is deemed to be in the best interests of the child.

Under the law, in France as in the UK, both parents are still financially responsible for their children, even if they no longer live together.
Each of the parents must continue to contribute towards the child’s maintenance and education.
If you’ve had children together, one of you may need to pay maintenance to the other who is the child’s ‘main carer’. Most of the time, this contribution takes the form of maintenance paid by one of the parents to the other.
In the UK parents can either talk it over and reach an amicable agreement together, or if that fails you can go to the Child Support Agency (CSA). The CSA will work out how much is due and can even collect it for the ‘main carer’.
With an arrangement using the CSA, child maintenance is paid until the child reaches 16 years old, or until they reach 19 years old if they are in full-time education (not higher than A-level equivalent). Child maintenance is normally arranged as a weekly, fortnightly or monthly payment.
There is no CSA in France and child maintenance is paid while the child is in full-time education and actively studying (there is no time limit as in the UK) OR until the child finds “un emploi normalement rémunéré” i.e. a job and not just a work placement.
In France child maintenance is ALWAYS a monthly payment. The ‘main carer’ receives money directly from the other parent. The child maintenance cannot be paid to the child himself even if they have their own bank account.
In France, if parents make a private arrangement, it will never be legally binding and therefore will never be enforceable. In order to make it legally binding, you have to get an Order from Court.
In England and Wales, a court can turn a private agreement into a legally binding Consent Order. In Scotland, a private agreement can be registered to make it a legally binding Minute of Agreement. Even if it is not registered it is legally binding, which is not the case in France.
Since child maintenance is regular, reliable financial support that helps towards a child's everyday living costs, it has to be paid 12 months per year, so even during holidays when the child is spending time with the parent who is not the ‘main carer’.

If your ex-partner lives abroad:
The UK has arrangements with more than 100 countries and territories that mean a person living in one country can claim maintenance from an ex-partner living in another. Reciprocal Enforcement of Maintenance Orders - or REMO - is the name used in the UK for this process. REMO claims are handled by the courts.