Paris no relation Gallia Belgica
History
Antiquity
According to Julius Caesar, the Belgae were the inhabitants of the northernmost part of Gaul. They lived in a region stretching from Paris to the Rhine, which is much bigger than modern Belgium. But he also specifically used the Latin word "Belgium", to refer to a politically dominant part of that region, which is now in northernmost France. Modern Belgium corresponds to the lands of the most northerly Belgae, the Morini, Menapii, Nervii, Germani Cisrhenani, and Aduatuci, who Caesar found particularly warlike and economically undeveloped. Caesar described this region as having strong kinship links to the Germanic tribes east of the Rhine. The area around Arlon in southern Belgium was a part of the country of the Treveri. 
After Caesar's conquests, Gallia Belgica came to be the Latin name of a large Roman province covering most of Northern Gaul, including the Treveri. However, areas closer to the lower Rhine frontier, including the eastern part of modern Belgium, subsequently became part of the frontier province of Germania Inferior, which continued to interact with their neighbours outside the empire. At the time when central government collapsed in the Western Roman Empire, the Roman provinces of Belgica and Germania were inhabited by a mix of a Romanized population and Germanic-speaking Franks who came to dominate the military and political class.
no relation