I wouldn't go as far, but the question would be, do you have the resources to put down the rebels yourself and does the military power come from you? Before I continue, I'm no medievist, so I sincerely invite discussion and to be corrected!
Now early kings of France didn't really have that kind of power, and indeed we see the power is really fluid, with France being kind of a loose confederation.
However, we do see the king of France being able to grant the whole of Normandie to Rollon, by his own authority, without this being an empty promise to be made de facto by force, like the Americas.
But after Philippe Auguste, the king has power in his name and rules. As in, he can knock heads without begging other rulers for help. The Pope couldn't do that, all he could do was ask others to intervene on his behalf. It's a bit similar to being part of NATO I'd say. You can ask but it's not guaranteed, and just because you're the head of NATO doesn't mean you control your members military
'We have heard that you are the sort of man who sends other men to do battle on your behalf- (implying weakness, for a true Akkadian king defeats enemies not by force of arms, but by the 'aura of dread' imbued by the Great Gods)' -Tukulti-Ninurta to Kashtiliash IV,,
This among other Assyrian provocations that were intended to demean Kashtiliash IV's (1232-1225 BCE)manhood and his piety to the gods broke the two century long Karduniash (kingdom of Babylon) geopolitical strategy against Assyria. For the past many decades, Karduniash had fended off Assyria through an unorthodox strategy. Assyria possessed superiority in many aspects to their southern rivals, namely in terms of military centralization and the mass conscription that Assyria utilized. Assyrian military mindset was by leaps and bounds, the most centralized and militarist in the Bronze Age, with the going trend that there existed only a few occupations in society, yet all were subsumed by the overarching Assyrian imperial mission of universal and total conquest.
Additionally, Assyria possessed ready amounts of soldiers and a fearsome and warlike nobility who clamored for war every year. In fact, Assyrian kings who did not wage war were said to be impious and could be in threat of losing their heads, as Shalmaneser V did in 722-721 BCE. Considering this, Karduniash worked under the conception that their enemy, Assyria was a foe too great to defeat in single pitched battle and too vicious to battle without special stratagems. However, Kardunaish possessed and developed a series of advantages with which to control, subdue and for a period, dominate the most formidable of all Bronze Age states.
The first of this was Karduniash leveraged its trade, prestige and armies to acquire series of loose vassals across the Zagros mountain ranges. These vassals were little more than independent kings who were acquired and ordered about by Karduniash for the sake of withholding Assyria and for gaining access to Babylonian goods and markets. However, these vassals did not serve just a military role, but a role in terms of acquiring and depriving Assyria of goods from the east, mostly horses. Hence, the famous statement to the king Kadashman-Enlil II 'in the land of Karduniash, horses are more abundant than straw and gold is like dust.'
Karduniash had acquired all sorts of soft powers and defensive, economic and prestige powers with which to combat superior foes, who in theory were Karduniash vassals (since the 1300s, the Assyrian kings, were in theory vassals of Karduniash, but were constantly recalcitrant and rebellious unless outright occupation). Such was the situation that when Assyrian kings went to battle with Karduniash in the 13th century, the Karduniash implemented a strategy of avoiding all confrontation in pitched battles and took to ordering its vassals to attack from the east and north while the Karduniash army would flee from Assyria and lead them into fruitless chases across riverways and deserts. All the while, Assyrian military command was, despite its mobilization, unable to maintain war for long periods of time due to the isolation imposed upon them by the trade sanctions from Karduniash. Hence Assyrian military units would despite victories in battle and holding clear superiority in all matters of military engagement, even in terms of logistics, at several points were forced to submit to vassalage under Karduniash.
Only whence Assyria both expanded north against the Hittites and other peoples north of Assyria, did the tide begin to turn for Assyria against its economically and diplomatically superior foe in the south. Assyria succeeded in goading Karduniash into pitched battle without any strategy other than engaging Assyria outright.... One can see where this story goes; the Assyrians massacred the Karduniash and established a vassal state over the region.
To put it into brief terms, the breaking of the old Karduniash schemes of holding Assyria, its northern and superior foe, in place, led to total and complete defeat. Yet, in prior times, it is difficult to argue that Assyria was not at least a reluctant vassal to Karduniash and precisely due to the effective geopolitical formula implemented by Karduniash.
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I present this example to you in brief as an exploration into the notion that there can be manifold schemes and stratagems to rule than simply 'marching to battle and defeating the enemy in a clash of blades!' It is with nuance and understanding that we embark upon the rendering of history as a world filled with diverse authority, systems and hegemony. Not always is it as the phrase goes 'they believe matters to be complex, yet it is the sword which is sharpened for the engagement' (-marshal of the Abbasid caliphate during the Mongol invasion of Iraq).
So my question to you is, is your opinion that the Papacy in order to enforce his authority, must do as Tukulti-Ninurta bid his rival to do? To march into battle himself, to march into Germany and enforce his authority? Or is it not a better strategy what Innocent III did in otl? Castrate the political and legal power of Philip of Swabia, divide claimants into three, send one to Sicily under Papal guard, throw the Welf against the Staufen and then compel with threats the new victor, Otto IV of Welf to come to Rome and prostrate. Thereupon, Otto IV did so and afterwards, recanted and invaded Sicily. It is at that point, after implementing all of his advantages, that Innocent III 'went for the kill' and brandished the sharpened sword and proved Papal hegemonic lordship over Europe....
1. Excommunicated Otto IV.
2. Placed the Empire under Interdiction.
3. Innocent III declared Otto IV bereft of the Kingdom of Empire, Germany, Middle Francia and Italy.
4. Declared Otto IV a renegade and called all men of his realm to take his head.
5. Declared the young Frederick of Sicily as Emperor of Rome and universal king of the composite monarchies
6. Promulgated an order fro Crusade upon Otto IV and any of his faction that maintains his royalty.
7. Raised a Crusader army in his realm and attacked Otto IV in the vicinity of Abruzzi and decisively defeated him in Italy, forcing Otto IV to flee to Germany and conclude an alliance with the beleaguered John Lackland of England so as to protect each other against the interdicts of Innocent III.
8. The Crusades led to Innocent III ordering Philip II of France to dethrone Otto IV, who already beaten in battle by the Papacy, was far weaker than normal.
9. France crushes the two renegade kings. Otto IV returns to Brunswick and submits to Innocent III and dies a sad man deprived of all honor. John of England is forced to kiss the feet of Innocent III (note, not of Philip II, it is clear that the one who was the true war leader in this instance, was Innocent III, not Philip II). Whereupon Innocent III affirmed himself as king of England and then returned the crown to John and sent him back to England as a humbled and weak vassal state. To use an American slang, 'France was the cleanup team.'
This formula is a system on a grand scale to a degree of what Alexander VI was implementing upon his own vassals in the duchy of Spoleto or the former Exarchate. Using all sorts of schemes other than simply marching about as a tyrant to enforce his authority in feudal terms. It is my contention, that all of France, Germany, Italy, Middle Francia and so forth were vassals of the Papacy to a degree similar to that of Ravenna. They may rebel, they may be only loosely held legally, yet it is still the case under my interpretation.
Furthermore, the Papacy ruled this confederation through a myriad of legal, spiritual, feudal and military means. It was not an empire like Assyria, who in order to assert power, had to march about with an army every year and assert power. Nay, the Papacy was a subtle entity, which played under the motto of 'it is no strength to slay enemies with the sword, much greater is the power and strength to convert your enemies, to hear your words in their mouths.' Most surely, the Papacy operated under the idea that the states of Europe were generally having resources in excess of the Papacy, but otherwise were manipulated and controlled by the Papacy. As well, there was always a sense of unity in Europe in the Medieval Era, that pervaded what we see now as national entities. The Papacy, acted as the most clear and sublime example of a universal lord over Europe, while the king of France and Holy Roman Emepror oft coveted such universal temporal aurthority; this is as Girogio Falco argues, the fundamental conflict of war, propaganda and economics for the soul of Europe in the Middle Ages, a battle for who was to be the universal master of Europe. Ultimately, none could 'breach the barrier' and the result was localism and insular relations between European states which was the prelude to nationalism and is the mother of our current world in relation to Europe.
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It should also be mentioned in passing, that the Papacy permitted the expansion of Philip II. If one observes the change in the borders of royal France, you will notice, certain lands are not touched in the slightest. These are the Papal direct holdings across France.... Which also, interestingly, increased after the expansions of Philip II, there was almost definitely a grand French royal-Papal closeness of proximity rarely mentioned. Such proximity was the foremost importance in the centralization of the French royalty and the assertion of royal feudal power over the excommunicated Angevins, the interdicted Toulousians and the other varied thoroughly rebellious lords of the realm who had been baskets of rebellion ever since House Capet arose.