Warning, the following are just some thoughts, suggestions and opinions. They aren’t cannon yet and might not be.
I think our bet for the PoD would be around John Lackland's reign. We would be needing to prevent the treaty of Paris that gave him his royal epithet, and large parts of his reign seeing that he had failures that were more systemic than anything. That is quite easy to do with a lazier PoD like another brother inheriting the throne.
In general, we can have as PoDs:
- John being born but having a different personality. In other words, another person with the same name and born at around the same time. Quite easy to do.
- Another brother inheriting the throne. Harder for it to end with an effective reign.
- The empire being split among brothers and later reunited through marriage between cousins or something similar. Even harder.
Then we would need a period of consolidation, only after that we could expand the lands of the Angevins.
Without John’s reign we would lose the Magna Carta. On the other hand, with an empire so diverse, it’s likely that some form of compromise would have to be reached to govern it effectively, it would likely have a lot to do with the inheritance practices as the Normans and the English preferred different approaches, with the former dividing the territory between children as it was with the Frankish Empire and the later having absolute primogeniture.
We would also change the fact that John was excommunicated and thus we could also, if there is a war in France, have the Pope favouring more the Angevin side than in OTL. Even then though, we would need to have the Holy Roman Emperor not opposing the Pope as much, since the HRE was on the side of the Angevins against the French. A weak emperor might be our best bet since a civil war might be too unpredictable and harder to archive, even when it has its advantages for the history. On the plus side, a civil war would weaken the HRE and we would need it as weak as possible so their intervention in France isn’t significative enough, so they can’t take lands and expand even more. Overextension in the HRE only would favour the Angevin Empire if it’s too much and the Empire is already weakened since the difference in population could make up for it.
The Angevin Empire would have a complex relationship with the Pope since the tittle of Emperor of the Romans (or whatever form it takes) would have to pass to them from the HRE. There are a lot of complications from that. An imploded HRE could be the answer, or one hammered down hard enough the title could be passed to the Angevins.
Other important thing, something to think about even if a very long shot. Temüjin was born in 1162. If the conception of John is our PoD, which is the earliest one I suggested, then it means the Mongol Empire could still exist even if vastly different than OTL. Let’s take that for granted for a second. Regardless of the Mongols expanding anywhere else, for example, towards China, we could maybe be having the Mongols raiding into the HRE. Maybe they could focus all their efforts west instead of east. It could be that the Chinese repelled them, partially or wholly. Whatever the case, let’s just say that Temüjin was able to secure his position as the Great Khan and expanded… Could it be possible or too many coincidences have to happen?