Once you have decided to buy, you must decide which ownership structure is suitable for you. This can be decided on between contract and completion (acte authentique) but you will need a suitable clause in the contract in case the names that eventually go on the final conveyance deed are different to those on the contract.
Aside from the purchase contracts, you may have concerns about your situation with regards to inheritance law (see the FAQ), residency issues, income and capital gains tax or other legal and tax issues – in which case you need to consult an English-speaking legal adviser who specializes in French property law.