There's a related recent discussion here. The existing populations certainly weren't completely displaced, nor is it likely that the number of newcomers would have made such an outcome possible or desirable: population estimates are hazardous, but even after the crises of recent centuries the western Empire probably contained upwards of 20 million people (down from perhaps 30m at its peak), the rest of Europe fewer than half as many, by no means all of them contributing to the movement across the frontier. Except in Britain and some border areas where migration was more intensive and sustained, the languages that emerged remained mostly of Latin origin: even in England, which ended up with a Germanic language, genetic studies have suggested an Anglo-Saxon input of perhaps 30%, in line with estimates of perhaps 100,000 settlers. The vast distances involved seem to support the impression that the most spectacular conquests were a movement of mobile groups rather than whole peoples: Germany too remained resolutely Germanic, suggesting that most stayed put.