Definitely a yearly property tax on the French side. I don't have any personal experience, but have heard the process is more convoluted on the French side. It sounds like you need to touch base with an island real estate agent, to look at some of these questions. Although I would actually not be surprised if you would have to pick an agent on the side of the island that you want to buy on, as it could be that an agent can only sell on their side of the island. Either way, as Pat said, please consider all the down sides, before you jump in. What is your ultimate goal? Is your ultimate goal to live on island full time? If so, and you have not spent a significant amount of time in a row on island--say 3 or 4 months--I would do that first, before you buy.

Best wishes!