I would guess that you're looking at maps of Capet France, around the turn of the millennium. This was indeed almost certainly the absolute pit of the authority of the French crown. To understand how the Capets inherited such a meagre domain, you'll have to go back to the last years of the Carolingians.

The Carolingians, tracing their lineage to Charlemagne, begin with a strong administration and a huge land under their command. However, by the end of the 800s, the family is in shambles; in the 880s, the major Carolingians gradually die off without heirs, leaving Charles the Fat in control of most of the Carolingian lands. (Ironically, this is the point in which most of Charlemagne's empire is reassembled for the first time in decades.) However, Charles the Fat does not outrun the family's bad luck; he falls ill, and he only has a bastard son and thus no legitimate heirs. He is eventually overthrown in a coup for the East Frankish throne by his nephew Arnulf weeks before his death. The next closest surviving Carolingian who would thus end up on the West Frankish throne in Paris would be... Charles the Simple, who was a whole eight years old at this point.

Clearly, Charles the Simple could not rule Francia at that young of an age, particularly as the Vikings were causing problems with their raids. The West Frankish nobility thus chose to elect Odo, Count of Paris, as king of Francia; Odo had successfully defended Paris against a lengthy Viking siege, and thus had the experience necessary to lead in a difficult time. He was not elected without some factional infighting; the decision was not unanimous, but it was enough, and Odo became king. Now, Odo was not a Carolingian; he traced his ancestry from Robert the Strong, and so he is often called "Robertian" when talking about heritage. Eventually, after failures with later Viking raids, the French nobility, which had already been lukewarm on Odo, revolted against his reign and ""restored"" (as the charters say) Charles to the throne... for a price. As Chris Wickham in Illuminating the Dark Ages, 400-1000 says:

Civil war followed; Odo and Charles made peace in 897, and Charles was recognized as Odo’s heir, in return for Odo’s brother Robert being recognized as in sole control of the family counties and monasteries between the Seine and the Loire and around Paris. When Charles succeeded as king (898-923), he was thus cut out of a large section of the traditional royal lands in the Paris region. The counts of Vermandois, Heribert I (d. c. 905) and his son Heribert II (d. 943) - themselves distant Carolingians, for the former was grandson of Bernard of Italy - had occupied most of the royal properties in the Oise valley north of Paris, too; Charles was left with Laon to the north-east as a political base, extending to Reims whenever he could.

Thus, Charles was put on the throne by a rebellious nobility, who had exacted a harsh price for their support and who now tightly ringed Charles's land. It is at this point that the nobles suddenly begin being granted hereditary rights to their lands, thereby more deeply entrenching them in their regional power scenes. Again from Wickham:

In the case of the lay aristocracy, this land could be then added to by honores: royal-confirmed offices, such as counties, and benefices. These were given by kings and could, for a long time, be taken away again. Werner of the Northern March is a case in point: he lost his offices and benefices in 1009, though he kept his properties. It is not that the king/emperor could not confiscate his properties as well; this nearly happened in 1013, indeed. But under normal circumstances (that is, anything except treason, and sometimes even then) kings would leave aristocrats with their full property even when they fell out of favour and lost the rest. We have seen in previous chapters that aristocrats always sought to preserve counties and benefices for their sons, and very often succeeded, including under Charlemagne. But until that inheritance became a right, kings kept strategic control of this large sector of aristocratic wealth and power. In most of the post-Carolingian kingdoms before 1000, and also in England, such rights to automatic succession in counties/ealdormanries and benefices only existed on political margins, such as, in England, Northumbria, or, in Italy, parts of the march of Spoleto in the far south or Piemonte in the north-west. The major exception to this was West Francia, where such rights were in effect extended to nearly every duke and count in the decades around 900, with catastrophic effects on royal power. When this ‘patrimonialization’ process occurred, of course, aristocracies hugely increased their practical control over wealth and local patronage powers, for they could now add ex-royal land and local political rights to their own properties, as long as they could keep control of them in the framework of local rivalries which were no longer moderated by kings.

It is important to note that hereditary rights to a county or a duchy made it much more difficult to remove a family from power. This particular era was not an era where a rigid constitution and a massive dense legal bureaucracy existed like it does today; custom and tradition weighed very heavily, and agreements between the crown and regional powers could be individually made ad hoc with no real legal boundary to protect either side. Once a family was able to establish its roots, it became much harder for the king to manipulate the arrangement of power. Wickham states: "[Charles] and his successors had no power to choose counts and dukes, unlike the kings of East Francia and Italy; no tenth-century West Frankish king had any significant effect on the succession of a major county or duchy, unless its ruler died without heirs." This, as the above quote says, was quite unlike the situation happening in the east and in Italy, where rulers remained able to shuffle around counts and duchies at their pleasure.

To give an example of how deeply a hereditary countship may be entrenched, Robert Fawtier in The Capetian Kings of France, Monarchy & Nation (987-1328), recounts a letter written by Eudes II, Count of Blois, who is feuding with Robert the Pious and reminds the king of his claims to his territories: "For consider my ancestry: by dint of it, I am, thank God, entitled to succeed to the counties of Meaux and Troyes. Consider the fief you have bestowed on me: It was not granted out of your royal fisc, but is part of the lands which have come down to me by hereditary right and of your royal grace." Because his ancestors had ruled the lands, it is not just a privilege for Eudes to be in control, but a right by blood, one that he did not think the king could just take from him, entitled as he was.

Why would Charles give up rights and territories like this to the French nobility? Couldn't he see that it was undermining his own position to have a dismally small domain and for his nobles to be accumulating rights and powers on their own? Well, of course. But given that he came to power only with the support of a noble rebellion, and those nobles now hemmed him in and were in many ways becoming more powerful than him, he must have been very aware that his position was not assured, that he was in fact in a very dangerous position, and that he could be removed if he became too much of an issue. He needed those nobles to support him, and thus he was forced to be generous, much to the detriment of the crown's position.

So, up to this point: Succession troubles of the later Carolingians led to civil war which led to weak kings who had to give away power to the nobility and who could not enforce their own will independently.

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