The father of my child, a minor, has passed away. He was a big spender and I know that he had applied for an over indebtedness procedure. I would like to renounce the estate in my child's name. What is the procedure?

To renounce an estate in the name of a minor, you must first obtain the agreement of the family affairs judge acting as guardianship judge at your local court. To do so, you need to send him or her a request using the Cerfa form n°15811*03.
Once the authorization has been obtained, you must send a renunciation form in your child's name (Cerfa n°15832*05) to the clerk's office of the judicial court in the place where the succession is to be opened, which in principle corresponds to the deceased's last place of residence.