Like any French citizen, you will have to pay certain fiscal duties at the moment of the purchase. In practice the notary will pay all taxes , stamps and recording fee and fill in all the compulsory administrative forms on your behalf.
After the sale you will have to pay two kinds of taxes:
Local taxes and income taxes generated from the eventual rental of the property. Local taxes and divided in two taxes.

The tax is due if you are the owner on the first of January of the year in question. It is fixed for the whole year, according to the status of the property on the first day of the year.

This tax is to be paid by the dweller, whether he is the owner or not. An owner-occupier has to pay tha land tax and the local tax. Usually the local tax is approximately about the same amount of the land tax.

The local authorities fix the tax rate of these two local taxes, usually the town. Although they may vary from one place to another and from one property to another.

Since France has signed convention with the U.S.A you are not subject to any fixed-sum taxes, from the mere fact of owning real estate in France. On the other hand you are obligated to declare to the French IRS any income from French origin (for example rental income.