You can write to the mairie of Royat for information about the death and burial. Here is the address:
Mairie de Royat
46 BD Barrieu
Here is the official website of the city:
Ville de Royathttp://www.royat.fr/
You will want to ask for a « copie intégrale » of his « acte de décès » (complete transcription or copy of his death record). Of course, you must give his exact date of death. However, there are no restrictions to obtaining death records, whatever your relationship.
Royat is a small town, about 4500 citizens. You should receive your reply in less than a week after you make your request. They reply quickly. (Of course, write in French.)
By the way, I would not imagine that his grave would be difficult to find in the cemetery of a town of this size.