All in the title.
https://en.wikipedia.org/wiki/List_of_oldest_buildings
The oldest being Barnenez, Tumulus de Bougon and the Tumulus de St. Michel, all located in the Northwest of France, all from the 5th millenium BC. What was so special about this region and time that preserved these structures?
This is really more anthropology than history to be honest, but an interesting question nonetheless.
All societies placed great importance on death and burial. Most of the buildings that remain from prehistoric times are tombs of some sort. From Japan to North America to the mounds you mentioned in Europe, it seems building burial mounds is just intrinsic to human nature. Why death and burial are so important to humans is really more of an anthropological question that I can't really answer in depth.
These structures in France are the oldest buildings we know about. If you look at the Mound Builders in North America, a lot of those weren't excavated and studied until the 1960's. The difficulty with mounds is that they get buried or crumble and often start looking like regular hills. Japan and South Korea are two of the most densely populated and developed societies in the world, yet they're still uncovering new tombs all the time. So there could be thousands of older buildings that have been buried that we don't know about because they are in poorer countries where archaeology and history are not priorities or they have simply been buried by time.
I'm not a geologist, but in the specific case of France the building materials could also be a factor. If you look at that map in the link you will see that northwestern France has crystalline rocks. This includes rocks like granite, which are much more durable than other building materials. That could factor into why these buildings have lasted longer.
Climate could also play a role, as that region of Europe has a Marine West Coast climate, which is very mild without weather extremes and is not found in many places. Weather extremes are often the cause of building dilapidation, so the lack of them helps preserve buildings.
I hope this wasn't too speculative for /r/AskHistorians, but it is quite difficult to give a concrete answer to this question since we have no direct records of these times.
In addition to what has been said there are a few more things to take into consideration.
The buildings you speak of are the oldest still standing structures. We have plenty of evidence of structures from earlier points in time. In fact, we have entire cities. Catalhoyuk in Turkey is a fantastic example. The entire area of Turkey and the Eastern Mediterranean has a whole host of sites that are earlier than this where we have proof of structures.
In the British Mesolithic we have the incredible site of Starr Carr which has evidence of the oldest building in Britain. This is some 4,000 years before the examples you site.
If you want to talk about sites the big classic is Gobekli Tepe, which is a ritual complex in southern Turkey, dating about 5,000 years prior to the French ones. They haven't excavated the entire site but based on information from the local practices in the region and evidence of human remains they're reasonably confident there are burials somewhere on the site.
Of course, these were building for many different purposes. But the point is that the purpose of the French structures aren't that unique.
Mankind has always seen death and burial as very important, which is a bit of a cop-out to be fair. But it's the best thing we can say with absolute certainty. The French examples are no different than any other. It's just the rituals themselves that differ. I don't specialize in death and burial though so for me it's hard to delve into the current research on this matter. What I can tell you is that there is both significant overlap and significant differences between different groups at different time.
Hawkes' Ladder of Inference, which I'm quite fond of as it fits my bias, tells us that one of the most difficult aspects of archaeology for us to infer is religion. We can look at the material remains, we can look at how they performed certain rituals and such. But it is near impossible to say why. Because there is very rarely physical evidence of why. So the question itself is one that's heavily discussed.
Furthermore, again to echo /u/theskyisnotthelimit there are a number of places in the world which has received significantly less archaeological attention than France. We know of literally thousands and thousands of sites in Europe because we've done extensive survey there. Most of them haven't been excavated, but we know about them. The same can only be said for smaller, more localized, areas in say Africa and Asia.
Why did the French examples survive so well? In addition to /u/theskyisnotthelimit you have to consider the fact that no one, or nothing, toppled them over. Simple as that. These are large, solid, structures that weren't made from mudbrick or any other types of man-made materials. It's like a bunker made from stacked stone. They're also quite low to the ground by comparison.
And one thing I noticed just in the wiki articles is that they don't talk much about the people that built them. And to me ritual complexes without putting them in a regional context are less interesting. This isn't my time period or my region, so I'm sure someone has done this somewhere. So if I were you I'd look more at archaeology surrounding the people that actually built them and less on the monuments themselves. It might give you some insight.