Child with F+ card no social support

If the child's birth certificate shows a Belgian father who is now dead, the child will inherit from the father. The rules of inheritance here are clearly laid down by law. Take advice from a notaris. The first visit will be free if you simply seek advice but the notaris does not actually do any work for you.
Otherwise ask at your commune and/or your mutuelle.

The child has a Belgian parent, so should have Belgian nationality. Why is this not the case?
F+ = non-EU national with permanent residency. The mother should also have an F+ card. Therefore, if there is any entitlement to financial assistance, the mother should be able to get it for her and the child. That will include family allowance and tax breaks an might include financial assistance through the OCMW/CPAS.
The child itself is not actually entitled to anything.