Actually, I bought my son a property last year - in his sole name as he was a first time buyer so avoided UK Stamp Duty. Simply for IHT purposes as I had downsized, e.g. I live for 7 years after doing so and he doesn't have to pay IHT on my entire estate. Even if I don't, it is a sliding scale downwards regarding IHT. SJ's parents gave her, her inheritance early in order to do the same and after 18 years, as far as I know - don't quote me, that IHT element no longer applies in the UK. Not 100% certain how it works in France.
My son's father and I divorced 25'ish years ago and his father made no contribution towards the purchase of my son's current property. Therefore, as my son is now a property owner, he obviously needs a will. In which he states that everything he owns goes to me - unless he gets married/has children in the meantime of course, if so, then his Will be need to be reviewed, of course!
Sadly and unfortunately, I have known a few parents whose children have died before they did.