Starting in the 2nd century, the Roman empire began to very slowly evolve backwards. Instead of expanding, it contracted.
In Britain, Roman Legions left first the West and the North (383 AD) and then the entire island (406 AD) to fend for themselves. The troops were needed in Gaul to fight against the Visigoths under their leader Alric, who had crossed the Rhine river and were besieging Rome itself.
The result were barbarian raids all over Britain, and later the Anglo-Saxon invasion of eastern Britain.
https://en.wikipedia.org/wiki/End_of_Roman_rule_in_Britain#/media/File:End.of.Roman.rule.in.Britain.383.410.jpg
On the continent, Germanic tribes started invasions into Roman territories in the middle of the 4th century. In 406 the Vandals, Alans and Suebi crossed the Rhine and invaded Gaul (Gallia).
https://www.vox.com/world/2018/6/19/17469176/roman-empire-maps-history-explained
(insert: fall of the Western Roman Empire, 476 AD)
In Gallia, Clovis I (in his language frankish: Hlodowig) defeated the last roman ruler Syagrius in 486/487 in the Battle of Soissons and created Francia. In 508 the city of Paris (lat. Lutetia, later Parisius) became its capital. At that time, Paris was essentially the Île de la Cité with some unprotected huts on either side of the river. (https://www.lookandlearn.com/history-images/M806632/Paris-in-the-5th-century) No reliable records of its population exist, but it was likely just a few thousand or in the low ten-thousands.
In 500 AD, much of the technology and culture of Rome is lost. Many of the old buildings, from houses to stadiums, bridges and aqueducts, are still standing, but the people no longer know not just how to build them, but even who built them. The invading tribes have no more interest in them then they have in the forests and mountains - they are simply there, maybe the gods of old put them. Who knows?
Urbanization especially went backwards. Rome itself, once a metropolis of an unimaginable 1 million inhabitants during the 1st and 2nd century, when the Roman Empire had its greatest extent, has dwindled to around 50,000. Other cities in the Roman Empire had been utterly abandoned.
Population as a whole dwindled and the wars, plagues and famines helped it along.
For a time, Theodoric, king of the Ostrogoths, ruled a kingdom that included Italy, Gaul, and Spain. After his death in 526, the empire of the Ostrogoths was shattered, and changes took place which led to the rise of independent Germanic kingdoms in Gaul and Spain. In Gaul Clovis, the king of the Franks, had already established his power, and in Spain a Visigothic kingdom with its capital at Toledo now asserted its independence.