My mother has a notarised lasting power of attorney (mandat de protection future), and I am her attorney. She used to make regular monetary gifts to her grandchildren, and I am continuing this practice. The notary says this is not allowed. Is he correct?

Yes. The law prohibits the attorney from carrying out acts of gratuitous disposal (such as a gift) on behalf of the protected person without the prior authorisation of the guardianship judge (Article 490 of the French Civil Code)