German origin of the word "Gaul"

The word 'Gaul' itself seems to be derived from the tribal name ‘Wolkai’, written ‘Volcae’ and probably pronounced locally ‘Ghwalk’ [1]. This tribe lived in the south of modern France since (at least) the 5th century BC. Derived are Welsh in English and Waal in Dutch (Wallonia). The Romans, having difficulties in pronouncing ‘Ghwalk’ changed it early on into ‘Gaalk’, or Gallic. The word is possibly related to ‘to walk’ (the walkers). The name could refer to a German tribe (better: migrants) which had migrated to, conquered and settled in the south of Gaul long before they came in contact with Rome and written history. The West-Goths or Visi-Goths would do the same in the 5th century AD as did the Franks one century later. The region is indeed very attractive [2].

The word Gaul refers to its Germanic rulers, as does 'France' refers to 'kingdom of the Franks', also people of Germanic origin.

Initially, during the Roman republic, 'Gaul' meant the south of France (Gallia Transalpina) and the north of Italy (Gallia Cisalpina).

The Germanic Volcae must have conquered at first Gallia transalpina (from the Roman point of view, at the other side of the Alps) and later Gallia Cisalpina (on this side of the Alps), introducing the name 'Gallia'. Later, this realm fell apart in smaller ones. In 387 BC the Italian Germano-Gaul Brennus ("chieftain") sacked Rome. His famous words were "Vae victis!" (something like: Weep Losers!).

In yellow: extend of Occitan-Romance around 50BC
In brown: the greatest expansion of Occitan

In the original Gallia regions, Brythonic (Gaul, Celtic) was early on replaced by Occitan-Romance [3]. This process probably started around 1000 BC and happened in parallel with the replacement of the Etruscan language by Latin.  Etruscan died out around the time of Caesar. After the conquest of both Gallias by a Germanic people, maybe around 480 BC, only the aristocracy of German descent maintained its German language in the beginning, before their complete integration.

Brennus: The word is widely supposed to be 'Celtic' (Brythonic or para-Brythonic). But I demonstrated in the previous chapter that the Galatian-Celtic Brennus (281 BC) was a German [4].
The alleged Gallic Brennus (387 BC), who sacked Rome, was therefore also of German origin.

The north of France (north of the language border) was consequently NOT Gaul. Its population refused to be called 'Gauls' and preferred the qualification 'Celts' (wrote Caesar). But the Romans generalized the term to the north, even up to the Rhine border, after its conquest. The clearly Germanic tribes on the west bank of the Rhine and in Belgium were qualified by Rome as 'Gaulish'.

The Romans didn't link this to a specific language. It was about administration. It was like we say 'Europeans', thus not implying a specific language. This explains why the Treveri (people of Luxemburg) were also qualified as 'Gauls', despite their clear Germanic language.
Trier, the Treveri civitas (place of Roman civil administration), was the capital of the Praefectura Gallia (Spain, Gaul, Belgium, Britain - the notion 'Gaul' was expanded from Gibraltar up to modern Scotland!) during the late Empire. The Praefectura was ruled by a co-emperor.

Today, most historians qualify the language of the region between the Loire and the Somme rivers as 'Celtic' or 'Gaulish'. The same 'Celtic' language was allegedly also spoken in the whole of Britain and Ireland. Some believe that this 'Celtic' language was spoken between the Pyrenees and the Rhine, or even beyond, maybe up to the Elbe river. Some think that at a certain moment, the Celtic language was spoken in a region stretching from Ireland up to the Black Sea. All that is wrong. Do not confuse people with culture. 

At the end of the Roman Empire, the real language spoken south of the Loire was Occitan-Romance, which is a synonym of Gaul. North of the Loire, initially para-Brythonic was spoken, a language related to Brythonic (but heavily contaminated with Occitan and German words) and that chenged later in 'northern Occitan', which evolved to become French. Pure Brythonic was spoken in Armorica and in the west of the British isles. All people north of the Somme river spoke a Germanic language as did the regions Lorraine, Alsace and (greater) Luxemburg.

 'A Celtic people' never existed, only populations who had adopted the Celtic art and culture. They spoke languages as different as Brythonic, Occitan-Romance, German and their many sublanguages.