Yes. A future protection mandate does not prevent the protected person from disposing of their property with the assistance of their agent. However, Article 490 paragraph 2 of the Civil Code requires the agent to obtain the authorization of the guardianship judge to "perform a disposition act for free." The contemplated donation falls within the scope of disposition acts.
Note : Since you are both the agent and the beneficiary of the donation, if you accept this donation, the judge might appoint an ad hoc administrator to represent your father in this transaction.