Britain and Gaul had very different experiences following the collapse of the Western Roman Empire, for several different reasons. Firstly, even at the best of times, Britain was never more than a peripheral region in the Roman world: there were only a few major Roman cities there, large parts of the island had never been fully subdued, and the island was constantly being raided by people who had avoided Romanization.
Gaul, on the other hand, was a core Imperial region for most of its history - not on the level of Egypt or Syria or North Africa, perhaps, but every bit as important as Illyria or Hispania. Many major Roman cities were located in Gaul, including Arles, Lugdunensis, Cologne, and especially Trier. All four, espcially Trier, had been Western imperial centers (not exactly capitals, but close) at one point or another. Some of the wealthiest Romans in the Empire lived or had estates in Southern Gaul, and Gaul produced a huge number of late Roman officials and leaders, almost as many as Illyria. In a very real way, the Western Roman military establishment was based in Gaul, in Cologne and Trier, and the Germanic peoples living along the Rhine were the most Romanized of all Germanic peoples. Frankish elites of the fourth and fifth century were essentially just... Romans, with the distinction of their ethnic backgrounds. Many of them became powerful high Imperial officials, one became an Imperial regent, and one was even made an Imperial usurper against his will by his Roman troops. Most Frankish men served in the late Roman army of the Rhine, and lived their whole lives amomg Romans. The Burgundians who moved into south eastern Gaul were only slightly less Romanized, and by the time the late Alaric's 'Visigoths' were settled in Aquitaine they were a multiethnic combination of second generation Gotho-Roman immigrants, slaves, and disaffected Roman soldiers who had spent their entire lives in the Empire; they were as Roman as anyone outside of the elites.
When Western Imperial power collapsed, Roman society in Britain was soon overrun: all of their Roman troops had been pulled out of the island 50ish years earlier by various usurpers, they were being continuously raided by Picts, Scotti, and Irish peoples, and large numbers of only-slightly-Romanized Angles, Jutes, and Saxons were beginning to settle along the Eastern Coasts. There is a tradition that the Romano-Brits fought back to maintain their independence and way of life (the Arthur/Aurelius Ambrosius legends) but in every version they lose, and there are references to a mass exodus of Romano-Britons from the island to Gaul/Brittany under a king named Riothamus (Arthur, again?) possibly in response to a call for aid from Aetius or Majorian in the last decades of Western Roman Imperial rule (another story in the Arthur legend has him rush off to fight for a Roman Emperor and die doing so) but the island proper is pretty quickly carved up into a small number of mostly pagan celtic tribal kingdoms in the parts of the island that were least Romanized on the one hand and a bunch of thorougly pagan Germanic speaking tribal kingdoms in the old Romano-British heartlands on the other, Angles and Saxons and Jutes who have not been significantly Romanized and who will turn out to become the rulers of the majority of the island in the long run.
On the other hand, in Gaul, the collapse of Roman Imperial power sees the local Gallo-Romans turn to the nearest, most-Roman source of military power they can find to defend themselves from less Romanized raiders LIKE the Angles, Jutes, and Saxons who just migrated to Britain. In the North, the local Gallo-Roman elites in Trier and Cologne and so on, many of whom were Romano-Frankish already, or related to them, turned to the surviving components of the old Roman military establishment on the Rhine: Clovis' Salian Franks. Clovis himself may have been supreme Roman commander along the Rhine in the 460s, and his father definitely had been before him. Clovis was every bit a Roman elite, but he was also a king and general of a huge number of Romano-Frankish soldiers, and the local elites felt comfortable with how Roman he was. The same was MOSTLY true of Roman elites in south-eastern and south-western Gaul, although both the Visigoths and Burgundians experienced some local resistance in the early decades of their rule, before the Western Imperial court vanished. But within a few decades, Clovis and his Franks would defeat all their rivals and become the sole power in Gaul. As the Merovingians, they would rule an extremely Roman post-Roman state for three centuries. The Franks had no desire to unmake or dissolve Roman civilization when they took power in Gaul, because to a large extent they had become Romans, or at least as Roman as anyone outside of the upper elite in the late Empire, before the Empire fell. They spoke Latin, they were Christian (and quickly became Catholic) they understood Roman style law and government, and the cultural union the Franks and Romans in Gaul achieved created the foundation for the most successful post-Roman state in Western Europe.