Whenever I read about the administration of Western Medieval kingdoms, books often describe an overly simplistic “feudal pyramid” with the king at the top and the nobility under him as vassals. This is also often accompanied in the text by an explanation that the vassals are entitled to all tolls and rents on these lands, while the king is expected to live off his own demesne.
The implication is that all nobles are on tax free lands. But then who runs the castles and towns of the royal desmense?
I’ve read that by the time of Philip Augustus, officials such as seneschals take on judicial and taxation responsibilities in the demesne, but what about prior to that in late Carolingian times or during the reign of Hugh Capet? Who were these demesne royal officials? Were they considered nobles? Were they paid in lands like the greater nobles or paid a portion of the tax?
Frankish administration is, happily, better-recorded than one might think. The Franks employed an army of bureaucrats to administer their affairs. I think one of the figures you are searching for may be the Mayor of the Palace; a kind of manager of the royal household during the Merovingian period. They were certainly considered nobles, especially during the seventh century, when the offices of Mayor became hereditary. In 751, Pepin the Short, Mayor of the Palaces of Neustria and Austrasia, was proclaimed king with the support of Pope Zachary, thereby founding the royal Carolingian dynasty. I do not recall ever seeing a reference to how they were compensated, but I think it's fairly safe to say that, considering their power, they had their fair share of lands and tax revenues, regardless of how they got them.
Another position that should be of interest to you is the Administrator of the Fisc or the Master of Coin, who administered the system by which the revenues from the royal demesne were generated in the Carolingian period. I know of only one known Master of Coin: Engelram (c. 810 - 877). He was a noble (specifically, a count), and held many extremely high offices under Charles the Bald, but little is known with any certainty about his land holdings, and nothing is known of is parentage.
Sources that may be of interest to you include anything written by Ian Wood or Janet L. Nelson, the latter having translated the Annals of St-Bertin (Manchester: Manchester University, 1991), from which comes some of our information about Engelram. Wood's Merovingian Kingdoms: 450 - 751 (Abingdon, Oxon: Routledge, 2014) is an excellent introduction to the whole of pre-Caolingiana, including details of government and some administration. If you have Latin, the Monumenta Germaniae Historica is just about as good as you're going to get for primary sources, but you really have to know what you're looking for, and there's far too much for you to just skim.
There is also the Merovingian Lands Project by the Foundation for Medieval Genealogy, which, while I wouldn't necessarily consider it a citeable source, might help you place individuals that you encounter in primary source documents. I hope this helps.