The issue is that you're assuming that the land was returned to the "native people". Keep in mind that what is now Britain, France and Spain had been in the Empire for centuries. Spain especially considered itself an integral part of the Empire and it is unlikely that they would have seen an Imperial retreat as liberation.

An example of this comes through the legal frame work of the time. For most of the former imperial provinces the local peoples were considered to be Romans whereas the Invaders, Visigoths, Franks or other groups were considered different. For this reason they held separate legal codes and which ones were applied were based upon who the participating parties were. From this it is potentially the case that the local were seen as Romans by the Invaders, but did not see themselves that way. But it is worth remembering that these people had been apart of the Empire for centuries and while they had their own local traditions that still remained, it is hard to imagine that they would not have identified with the Empire. Spain is an especially special case as the Iberian Peninsula had been a core part of not just the Empire but also of the Roman Republic. Their people sat in the Senate, later on their people went on to be known as the best Emperors that the Romans ever had. It is likely that when the Empire withdrew from many places it felt less like they were free of imperial control, but rather that they had been abandoned by their own.

Another thing to consider was the Legions. They had changed a great deal from the times of Caesar. Likely during the reforms of Diocletian, the structure of the army was changed. Instead of all armies being standardized Legions, they were instead broken into two different kinds of Army groups.

The first and smaller groups were the Comitentensis. These were highly mobile units that were made mostly of cavalry units and were considered the Elite of the Empire. They were positioned strategically near areas of danger and could be moved around as necessary. Their goal was the rapidly respond to any threats and land killing blows.

The second and far larger group was the Limitanaei, these were border troops. Stationed along the perimeter of the Empire and were intended to fight off smaller groups of raiders or Invaders. They were also used to hold back larger groups and provide time for the Comitentensis to arrive. When the mobile troops arrived the Limitanaei could then support the elite soldiers in battle. The important thing for your question is that the Limitanaei did not get moved around unless in dire circumstances. These soldiers lived in the area that they were station and were often recruited from that area as well. Their families were often with them. When it is said that the Western Empire retreated from areas like Britain and Spain, it is referring to the removal of Comitentensis army groups. It would be hard to imagine Limitanaei soldiers abandoning their homes due to an Imperial order and it is hard to imagine the Imperial court having the resources to withdraw the hundreds of thousands of individuals that would have been necessary to bring back the Limitanaei.

To answer your question more directly. The native peoples would have seen themselves as Romans and many of the troops would have remained. They would be absorbed into the barbarian states that replaced the imperial administration. So much of these border troops would have been considered Foederati anyhow and would fit in nicely to the barbarian armies of the Franks, Visigoths and Ostrogoths