If you own property in France it is a good idea to write a French will, as under current legislation, French law governs matters of inheritance of French property.
Under normal circumstances, even without a will, inheritance can be fairly straightforward if you are married and have children, as the children automatically inherit. In the exceptional case of early death, your 'ascendants' (parents) are also among a small group of what the French call 'preferred hereditaries'. Following them, brothers and sisters are involved, and so on.
Complications can arise in the case of second (or more) marriages, and if there are children from previous marriage(s), and whether for example the children have been formally adopted or not. Dying without making a will can be complicated for those left behind to sort things out.
The simplest form of French will can be handwritten (known as a 'testament olographe') and your local notaire can give you a form of words in French. The will is then registered and deposited with the notaire - it helps to make photocopies for any other people concerned - and all this can be done for less than 100 euros. More complex wills are typewritten and drafted formally, sealed and deposited with the notaire as before (probable cost around 500 - 1000 euros).
If you are single and/or without any prefered hereditaties (parents, children) you can leave your estate to someone outside the family, nominated in your will. Unfortunately, they suffer high levels of inheritance tax of 60% on your estate (unless you were in a civil union such as PACS recognised by the state) but at least they can take the remaining 40%. Without a will, the French state could intervene and take everything.
When buying your French property it is a good idea to take professional advice on how the purchase contract is worded, in order to protect the surviving spouse on the death of the first partner. The notaire can advise on this and other matters related to French inheritance.