I'm not sure centralized is a fitting word for a feudal state. More "bureaucratic", possibly and certainly more united.Out of curiosity, in that scenario, given the greater centralization of England, migh Louis VIII successors prefer to rule in England, where the tax base is greater, leading to the French nobles attempting to free themselves from this "English" king, who attempts to impose English centralization on the French nobility?
For the residence : I think that eventually the Capetians would stay more in their french holdings for several reasons.
1) They used to. That looks pretty dull, but in a time where uses can be as strong as law, it counts
2) Paris and their holdings in France (here, as part of northern half of the kingdom) are rich and really populated (once century later, Paris became the first city of Europe and Christianity as a whole)
3) You'll have acculturation, but clearly, Capetians aren't going to "anglicize" themselves. Norman England kept many french features and without the Hundered Years' War pushing to a reject of these up to the court, they're going to last.
4) I don't think Capetians would try to impose themselves the Magna Carta and a powerful Parliment.
I'm pretty sure they'll eventually try to remove these in England when their power would be well ensured.
Furthermore, it could end with more territories belonging to Crown Estates in the Kingdom of France.
OTL, Louis VIII and Louis IX created several "appanages" : it was about giving lands to the sons that didn't inherited the royal title and possessions after the king's death. By exemple Poitou, Saintonge and Languedoc was given to Alphonse de Poitou, Anjou to Charles of...Anjou (isn't this amazing).
It allowed expanding royal influence, and as apanages came back to royal line if the cadet line of their holders is extinguished (even if they have other descendants), it allowed them to secure the possession of such lands in the kingdom.
I would likely see part of England being given as apanages instead of, say Poitou, therefore securing capetian influence, french presence, etc.
Given the great works Philip August did in Paris before the POD, I agree with you.I think this is an interesting question. What will essentially happen is you have two "rival" cities within the realm with London and Paris on either side of the Channel. Which city the king prefers will greatly affect history.
I'm inclined to think they will prefer Paris.
Great walls, one of the most important cities of Christiendom, and the Capetians already began to fix there a part of their administration and court.
Here, allow me to nuance.As I recall (and I might be wrong about this, so someone correct me if I am) Richard the Lionheart spent most of his life in France, not England, and that was something of a trend amongst other English kings at the time. If a French king stayed in France, it would play, I think, to the benefit of the barons as well as the king.
Richard was far more a Duke of Aquitaine than an English King. He's raised in the favour of his mother, and she basically made of him an occitan lord in many regards.
Being duke of Aquitaine, his policy isn't really different from his grand-father and the ramnulfid line. Knowing only latin, french and occitan, the kingdom of England must have looked like a foreign land.
I'm not sure you can say it was a trend : his father shared his time between England and France, Stephen as well. And maybe the fact Anglo-Norman culture was quite close to what existed in Anjou or N-W part of the kingdom played.
Of course, at this time Aquitaine knew more troubles than England, but that doesn't fully explain why he didn't even went a complete year in England during his reign. I'm not usually for explaining everything thanks to personal preference of historical individuals, but frankly, I think we're kind of forced to study this for this case.