By the Vth century, bureaucracy and nobility were kind of mixed up in the Roman Empire, more so as the imperial authority was unable to press core principes of Roman militia (civilian and military administration). Emperors had to legalize the territoriality of service (instead of being moved up regularly), the remuneration taken from part of fines (instead of a material compensation), and the permanence of service (instead of the ideal of a limited mandate).
Corruption and nepotism being generalized as the state authority was unable to really act against transgressions, especially on the lower part of the militia, officiales, public servants, who tended to inherit their position already; made emperors rather attempting to tweak them into new duties and habitus rather than ignoring them and increase collapsing risks.

In a same time military, civilian but as well religious service began to be fused by the early Vth century; provincial public servants appearing partialy with a military appartus, or bishop being considered as judex, officiales and often part of the local nobility.

The collapse of the state authority in Northern Gaul, its investment trough provincial palatial structures by Goths or Burgundians, or its takeover in Africa by Vandals (and later by Theodoric) had various effects : but roughly, trough fusion, polyvalence of offices best represented by the systematisation of Counts; a vibrant militia in places with most preserved state structures, a rather famished militia in Northern Gaul reduced to its simplest expression, and its disappearance in Britain or Pannonia, etc.

Roughly, in western Europe, the difference between Barbarian and Roman aristocracy is that they could be defined, the former as an aristocracy of trust and kin; and the second as an aristocracy of land and service. Overall, the militia reappeared in the late Vth and VIth under a new form, largely inherited from the Late Empire and its late reformation or accepted transgressions being the norm. They were not supplanted, and actually were necessary to the everyday build-up of Barbarian states on a Late Roman model : in fact, they might have been more structurally present than in the Late Roman Empire where you could maybe count 1 public servant for 5000 inhabitants as a best guesstimate.

What happened is that they slowly began to merge : it happened more quickly in Francia due to the absence of interdiction of intermixing and the Frankish conversion to Nicean Christianity; while such distinction laws and Homoian Christianity prevented it to happen as swiftly. But by the VIIth century, most people nort of Loire considered themselves Franks, Romans south of Loire, regardless of their origin. The same thing was achieved in VIIIth century with Goths in Spain or Lombards in Italy. Saying that someone might descend from Franks or Lombards give us no information at all about their ancestry in the Vth century, not when Roman families began to adopt germanic names (Gregorius -> Gondulf; Lupus->Wulf, etc.), neither as culturally-wise, Barbarians were already hard to distinguish from Romans due to their romanization.

By the VIIIth century, a potentes, a noble, was both an aristocrat of royal service and royal trust : his title and nobility wasn't yet tied to a political power where he was landed, but it was about to be one century later.

Arguably, the process was rather more confused in Italy : a more strict differentiation was enacted by Ricimer and Theoderic, the latter having more or less resurrected the senatorial aristocracy out of irrelevance; and it's the Imperial reconquest by Constantinople that led to the definitive fusion of military and civilian service in Italy.