In reply to Bojo:
Genetically, France is a melting pot of many races. However, your other claim does not follow. There are of course human races even today.
It is actually easy to find human populations that are genetically distinct and at the population level stable against introgression from other gene pools that they should be classified as races.
To avoid the whole politically charged issue of "black" vs. "white"*, the Han Chinese provide an excellent and obvious example: There are so many of them that in China there is very little introgression. Yes, Chinese also in China have children with partners from different ethnicities, but the overall pool is so big that the introduced haplotypes tend to be diluted out, rather than establishing themselves in the population.
This is obvioulsy not the case to the same extent with Chinese expat populations elsewhere, e.g. in South Asia or the US.
Size of the gene pool is also not the only mechanism that can stabilize a population against introgression, such mechanisms also include e.g. cultural, religious or social (caste!) isolation.
This is obviously a very broad brush description of a complex situation, but the simplification is not so bad that the overall picture is too far off.
In response to your opening post, I really recommend David Reich's book "Who we are and how we go here", which gives an excellent summary of the state of DNA based molecular anthropology as of a few years ago. The whole field still evolves rapidly, and you can essentially forget what was dogma even only 25 years ago.
CB
* just to say that there is no such thing as a "black" race. The genetic differences between certain African populations are much deeper than anything seen elsewhere. Not surprising given that essentially all modern non-African humans stem from groups migrating out of Africa, with a bit of admixture from various groups such as Neanderthals and two flavours of Denisovans.