Will Allah forgive one who falsely accused another, then repented, but did not seek forgiveness from the accused, and the accused refuses to forgive him unless he apologizes in person?

If the accusation is unjust, Allah does not forgive the rights of people unless they forgo them. A Muslim has the right to defend himself, but forgiveness and pardon are better, as Allah Almighty says: "The recompense for an evil is an evil equivalent to it. But whoever pardons and makes reconciliation - his reward is due from Allah. Indeed, He does not like wrongdoers" (Quran 42:40). And the Prophet, peace and blessings be upon him, said: "Shall I not tell you about the noblest morals of this world and the Hereafter? You forgive whoever wronged you, you give to whoever deprived you, and you connect with whoever cut you off."