Larmor-Baden has seen four holiday homes, a brasserie, a postal worker's residence and a garage go up in smoke since December last year.
Last weekend the priest's house, which was up for sale, was burned to the ground.
"The time has come for a name to be put on this arsonist.
This has to stop," said Denis Bertholom, the mayor of the seaside village of around 800 inhabitants.
Larmor-Baden lies in the Gulf of Morbihan on the south coast of Brittany.
Police said the fire-raiser targeted empty buildings only.
Story continues below…
Local prosecutors said a "complicated investigation" was under way but declined to provide any details on the lines of inquiry they were pursuing.