It's worth noting that what's entered our popular history as "the Barbarians invading Western Rome" in reality could be better described as "various Roman provinces establishing their political autonomy in the vacuum left by Imperial decline" in a great many cases. The Franks - who "conquered" Gaul - for example show up as a confederation of Roman client tribes in Belgica as early as the Third Century, and are often actively involved in Roman politics and military campaigns. The usurper Flavius Arbogastes who challenged Theodosius for the Imperial throne in 394 was a Frankish general, himself the nephew of Flavius Richomeres, another Frankish general, who attained the rank of both magister militum and consul within the Roman Empire. Arbogast's designs on the Imperial throne were stopped largely in part to the efforts of Alaric, who infamously led the "Barbarian" sack of Rome in 410, and an army of some 20,000 Gothic soldiers. Alaric's own campaign against Rome was largely motivated by the lack of recognition his army received despite their heavy losses propping up Theodosius. His campaign was also bolstered by a decision by the emperor Honorious to massacre the families of Gothic foederati already serving in Rome's armies, leading to the defection of over 30,000 men to Alaric's cause. Alaric even supported Roman pretender Priscus Attalus in 409 and 410 as his magister militum before Honorius' continued refusal to negotiate forced his hand. It's worth noting as well that Rome's gates were opened to Alaric by his allies, and his forces reportedly behaved themselves well on the Roman population.

By the time that Francia was established in the former Roman provinces of Belgica, the Franks had long been dominant figures in the region. Bishop Remigius of Reims implies that Childeric I, King of the Salian Franks from 458-481 and father of future unifying King of the Franks Clovis I, was the administrative chief of Belgica Secunda before he established it as his own kingdom, after an earlier career in the Roman army. While unifying Frankish kingdoms, it's worth noting that Clovis I worked hard to establish a close relationship with the Roman Catholic church, taking a Catholic wife, and converting himself in 496. Bachrach also suggests that, after conquering the Roman rump state in Gaul, Clovis actively incorporated it into his kingdom, assimilating entire sections of Syagrius' army into his own.

There are, of course, areas that were conquered, Britannia being one notable example. Of course, by the time the Anglo-Saxons begin to establish political authority in the British Isles, Britannia had long passed out of Roman Imperial control, but various successor governments had tried to establish themselves. If you believe Gildas and Procopius, then the Britons were indeed either killed in battle, slaughtered or fled en masse to Wales and across the English Channel to Brittany. Of course, the situation on the ground seems to have been quite different; certainly part of the British nobility did indeed flee into Wales and Brittany, but the "anglification" of what would become England was a protacted process that took over a century and was very much piecemeal. DNA studies suggest that, on the East coast, some 40-50% of the population may have been Germanic, but the collapse of the Romano-British successor states had been preceded by a particularly virulent plague, so these figures likely represented simple immigration rather than some kind of ethnic cleansing. Material evidence suggests that Germanic culture spread slowly Westward, but charter attestations suggest that as late as the ninth century, there were still ostensibly British sub-kingdoms operating under a wider 'English' hegemony.