My only son has passed away. He was single and had no children. He left a will in which he bequeathed half of his estate to me and the other half to an association. Was he allowed to disinherit his father?

Yes. Under Article 736 of the French Civil Code, when a person dies without children, spouse, or siblings, their estate is divided equally between their parents. However, Article 916 specifies that parents are not protected heirs (héritiers réservataires). Therefore, your son was legally entitled to exclude his father from the inheritance by testament.