After some research, I may be able to clarify some points.
It appears that, yes, Galles is a noun that represents a plural noun, as you showed before with the cnrtl definition.

However, you need to know that this word is part of some nouns that are only used with a plural form, and it has no singular form.
It appears this kind of unvariable nouns are called “plurale tantum” from its own latin word (I couldn’t find any french translation for this, and it appears to be the same for all languages). More informations here.

And finally, the reason why it is called Pays de Galles, and not Pays des Galles, is because this small detail changes everything.
In French, the part De Galles is what we call a “Complément du Nom”.

Saying Des Galles, would mean that this country belongs to the Galles (or the Wales, as a group of people). Sometimes, des is used as a part of a “Complément du nom” to express a relation of possession to some persons or some things.
But, using the word de instead of des, would mean something different than belonging to. It would then signify that there is some things or some persons in this place, but not with the idea of belonging.

That particular aspect would be found with something such as Bande de brutes, and Bande des brutes. Here, the first case means that this is a group of people made up of rude fellows in general. But saying Bande des Brutes, would mean that this is a group that is under the commandment of some people called Brutes, the Brutes being rude people or not. And the truth is, this little detail can change lots of things when you use it.

Have a nice day. 🙂

In pays de Galles, Galles is not the name of the people, or at least, it hasn’t been perceived that way any time since 1800. Since this question was motivated by the question of whether the Romanian name for Wales, Ţara Galilor (literally Country of the Gauls, or Pays des Galles) was a mistranslation, and this name first appeared in the 19th century, the answer to that question is that it was indeed a mistranslation.

To see this, look at the name of New South Wales, Australia, in French. It has been variously rendered as Nouvelles-Galles du Sud and Nouvelle-Galles du Sud. But if Galles meant Welsh and not Wales, it would have undoubtedly been Nouveaux-Galles du Sud. See Google Ngrams. French would not use a feminine plural as the name of a people (save for les Amazones). Google does find a few references to Nouveaux-Galles du Sud on the internet, but there are almost none in Google Books.

Interestingly, the Ngram shows that while most people treated Galles as a singular in Nouvelle(s)-Galles du Sud, there was a substantial minority that treated Galles as plural. This was most prevalent between 1880 and 1960, but it goes back to the 1790s, only a few years after the Colony of New South Wales was founded. Wikipédia says that according to Australia, officially Nouvelle-Galles du Sud should be singular, which may account for the decrease of the form Nouvelles-Galles after 1960.

“Galles” is a proper noun, which are not due to respect rules of orthography : in French, we say “les noms propres n’ont pas d’orthographe”.

Here, le “Pays de Galles” is like le “Royaume des aveugles” (meaning a country which contains blind people, or Wales people, or fairies and goblins) is singular: “le pays” remains the subject of the verb, not the people living inside it.