In the paper the author conducted a scientific study of the peculiarities of the performance of parental duties under the family law of the French Republic. It is noted that the French Civil Code uses the concepts of "parental authority" and "parental authority" to define the set of personal non-property and property rights of parents in the legal relationship between parents and children. French family law defines parental authority as a set of rights and obligations aimed at ensuring the best interests of the child. Parental authority belongs to the parents until the child reaches the age of majority or emancipation, for the purpose of protecting the child, ensuring the protection of his safety, health, protection of private life and his morality, ensuring his education and development, provided that the child is involved in making decisions related to exercise of parental authority, in accordance with the degree of maturity and age of the child; it cannot be carried out with the use of physical or psychological violence against the child. The main requirements for the exercise of parental authority (parental authority) by French family law are the proportionality of its exercise by each parent in accordance with the capabilities of each parent and the needs of the child); their joint implementation by both parents, unless otherwise established by a court decision in family matters; the emergence of parental rights and obligations on the basis of marriage and the birth of a child in it or within a year after the dissolution of the marriage, on the basis of a joint statement or a court decision in family matters; their termination in case of recognition of the father or mother as incapable, deprivation of parental rights or death; changing the conditions of their implementation by one of the parents is subject to prior and timely informing of the other parent and agreement with him. French family law defines the possibility of transferring (delegating) parental authority to a third party, a family member or trusted relative, a childcare facility or a departmental service for children at the request of the parents, a person, an institution or a service where the child is (while transferring (delegating) is not subject to the right of parents to consent to the adoption of a minor child). According to the French Civil Code, such management is carried out jointly by both parents, and in the case that parental authority is exercised by one of the parents - by the parent who exercises it.