My father has passed away. The notary handling the estate has only provided me with a copy of the will and informs me that he does not have the original, which is held by another notary. Is this normal?

Yes. The original of a will is kept by the notary who has custody of it, meaning the one who received it and filed it among his official records (Article 1007 of the French Civil Code). The notary you have appointed to handle the estate therefore only has a copy.