My father passed away a long time ago. My paternal grandfather has just passed away. My brother and I are his heirs. Can each of us benefit from the €100,000 tax allowance applicable to children?

No. When an heir has predeceased (in this case, your father died before his own father), his heirs represent him in the estate to be settled. For the mechanism of representation to apply, there must be a plurality of branches (in practical terms, your father would have needed to have brothers and/or sisters) (Article 752 of the French Civil Code).
However, the tax authorities exceptionally allow representation in the direct line.
Nevertheless, you share the allowance your father would have been entitled to (€100,000 ÷ 2) (BOI-ENR-DMTG-10-50-20 §50).