Four issues to be aware of when purchasing property in France:
1. The inheritance laws in France are quite different than those in Anglo-Saxon countries. You should review them.
2. There is a "Wealth Tax" that applies to the net French assets of non-residents above 720,000 Euros.
3. It is advisable to to come from a country which has a Reciprocal Tax Arrangement with France or you could incur other tax liabilities. (as an American you are good there.)
4. You should purchase the property in your own name rather than that of a company because it is unknown what future legislation may hold for company owned property in France.
Other than that the transaction looks rather straight forward. You will need the assistance of a "Notaire" and the costs of the transaction look to be about 6% of the purchase price. Commissions are paid by the seller but the buyer can pay them if they want to avoid paying the registration tax.