How do the children and other relatives inherit?
The children of the deceased exclude all other relatives (Art. 566 Cciv.). Children inherit from their parents in equal shares. It is irrelevant whether the children are legitimate, illegitimate or adopted.
According to the principle of representation, the children's descendants take their place if the latter is unwilling or unable to accept the inheritance (e.g. due to prior death).
If there are no children or other descendants, parents and siblings inherit in equal shares. However, the parents' share of the inheritance may not be less than half of the estate (Art. 571 Cciv).