What is the best thing to store French cheese, aluminum foil or plastic wrap?

I'll sing in the choir of cheese paper also. Formaticum is fairly easy to find especially if you purchase your cheese from a true cheese vendor. You can usually buy it from them.

I looked at Pegeen's link, and the suggestion of a cheese dome transported me back to living in Europe ages and ages ago. No one wrapped (or refrigerated) French cheeses at all. They stayed under the cheese dome, which made a regular appearance at the end of dinner.

I do use the cheese storage bags for most cheeses except Parmesan which I wrap with parchment

These cheese storage bags are great. And this link on their web site has good general information about how to store cheese.
http://www.formaticum.com/blogs/cheese-paper-101/2809722-all-about-cheese-storage

Parchment!

Neither. Cheese paper if you can get it, parchment or waxed paper if you can't. That said, I've been known to wrap cheeses in fresh plastic, but only for relatively short periods.