Is it a sin and a theft not to inform the authorities about a relative who receives a salary and health benefits in both his home country (a Maghreban state) and France, knowing about his chronic illness and his work in his home country?

It is not permissible for a person to conceal their true situation and obtain grants and privileges through deceit and trickery. They must repent from such actions. However, if they have disclosed their situation and not resorted to fraud, then there is no blame upon them for benefiting from what they are given by both parties.