Charlemagne's Francia, for all claims being the Empire (although less Roman than Christians) inherited relatively few features of the Late Roman state, and appear as a relatively weak and precarious state, in some aspects more so than Merovingian Francia.

The fiscal system inherited from the Late Empire was importantly changing since the VIth century, and the budget, from being based on direct landed tax, was more taking from indirect taxes (tolls, fines, etc.), plunder in the "outer" Frankish sphere, and the production of the fiscus, the royal public property (itself coming from the imperial property) which supplied the palace with its means of domestic and politic subsistence.

The Roman Empire was built on the necessary existence of a public service directly tied up to imperial network and management; originally waged trough the fiscal system, but public servants were gradually allowed (while it was previously illegal) to work on territories they or their families were landed or had any kind of influence, and were similarly allowed to live from obtained fines or benefices of their function. This waged public service was essentially gone by the VIIIth century, evolving more and more towards a fusion with court, militarized and land-owning elites since the VIIth century, first in peripheral areas where the Barbarian state wasn't really strong to begin with and relied on personal relations with the kings (essentially Germanic peoples and duchies such as Thuringia, Bavaria, Old Saxony, etc.) but creeping in Francia proper due to succeeding regencies and the rise of great families such as Peppinids/Carolingians.

The Peppinid ascendancy, in particular, seems to have favored the acceleration of this evolution : challenging the Merovingian rule by favoring what we call the vassality in their relations with Frankish aristocracy, meaning the use of personal oath and fidelity over a dwindling public service. This systematization of vassality was made possible in part by curbing down the "non-affiliated" aristocracy (either in Frankish sub-kingdoms, either in peripheral duchies) in wars and awarding other aristocratic families with the benefits of the wars (either landed or titled, both being increasingly mixed up), use of precarii (secularization of religiously-held wealth) and personal policy of prestige (victories against Arabo-Berbers, Frankish opponents, Aquitains, Bavarians, etc.: alliance with the Frankish and Roman church; etc.). As the fiscal system is essential breaking down since the VIth, public service is mostly payed in landed benefices, titles, lands, as the rest of the Frankish aristocracy itself tentatively identified to public service (which have the consequence to blur the difference at the benefit of a quasi-feudal nobility).

As Peppinids/Carolingians, in spite of their efforts, didn't quite reached the same transcendental status of Merovingian kings (which seems to have remained fairly popular, maybe so even after their extinction), they might have felt the need stressing they weren't just an aristocratic family among others by doubling down on this, and preventing a family pulling a similar attempt on them, especially as the number of ruling families is narrowed down to less than 100 ones. Eventually, more lands, more benefices, more plunder is necessary to maintain the state apparatus and when it is no longer possible and, worse, what exists is under the stress of raids coming from all directions, the whole imperial structure collapsed : but, under Charlemagne, it not yet the case and still on the better part of a political headlong rush.

Eventually, the court administration and bureaucracy remains limited, but it was already the case for Merovingians and, respective of their size (even if Carolingians were the first to conceptualise a polity this big since the Vth century), of the Late Roman Empire palatial network. It is furthermore limited by the lack of a diverse recruitment pool : the Frankish imperial aristocracy tends to monopolize the imperial service, and in spite of a special scrutiny by Charlemagne's envoys (the missi dominici), expelling faulty nobles is easier said than done. Bishops remained the best available alternative, especially as the best carriers of an imperial idea. While this one is less Roman than Christian, Franks having inherited the imperium previously held by "Greeks", Romans and Hebrews : Carolingians made great displays of their Roman titles, as given by the pope, either princeps or imperator (neither being that specifically "Roman" or making royal titles obsolete), the growing role of bishops in secular matters since the Vth century (contrary to their relatively secondary role at best in the Late Roman Empire and, of course, their absence in Classical Rome) is one of the foundations of the Frankish imperium especially in areas lacking a real secular management as in newly conquered Saxony. It's one of the reason why, when the Carolingians wanted to stress the display of the Empire as the successor of Romulus, Augustus and Constantine (but also David, Salomon and, in part, Clovis and Clothar); they did so trough the Church as Louis the Pious attempted himself (Charlemagne having probably not that of a clear imperial program, to the point the transmission of the imperial title don't seem to have been even planned before the 810's), Empire and Ecclesia being largely identical to each other, although on a line closer to the Late Empire and the Eastern Roman usages than classical Antiquity.

Overall, while the structures of the Late Roman Empire didn't entirely disappeared under Charlemagne, they were heavily transformed, under significant pressure due to changing social, economical and political situation since the VIIth century. Public service vanished within an aristocratic, landed and noble by birth rather than service, elite; which alone is enough to make the Carolingian state quite different in spite of tentative of mouth-to-mouth resuscitation trough edicts, power displays, etc. Charlemagne's Empire, in its administrative functioning was as different from the Late Roman Empire than it was from the classical medieval kingship, as well its own thing than an in-between.