Taxe foncière and taxe d'habitation are what folks in the US call "property taxes." France splits the taxes on a residential property into two parts - the part that relates to the ownership of the property, and the part that relates to who actually lives there.

Like in the US, both taxes are based on the "property value" - though in France it is based on the "rental value" of the home, determined based on a set amount per square meter of living space. But there are extra square meters added for various "upgrades" to the property - number of toilets, tubs and showers, central heating, swimming pool, etc. etc. The local mairie should be able to give you the details, including the current per square meter figure.

As to car tax, not really. Certainly not an annual car tax like in the UK. You used to have to buy a "vignette" (window sticker) each year, but that was done away with a few years back. You do have to have a car inspected every two years, and display a sticker showing it passed - so if you count that, there is a sort of car tax in the form of getting it inspected (and any work that needs to be done to keep it in passing condition).