Wouldn't the vassals of the EU declare independence?
They might not if there were attitude bonuses on both sides, a strong EU headstart in culture, and if none of the Vassals were strong enough to stand alone.
The EU is not a civ, but to make this work it would have to be treated as one. Therefore, Brussels (Belgium) and maybe one or two other cities would represent the core of the European Union. When you are trying to eliminate all but ~30 civ's in 2008, Belgium, Luxembourg, and Austria are not likely to make your top 30.
Then give each Vassal a strong attitude bonus toward the EU. Stretch it's economy a little thin. The individual civ's of the EU are not powerhouses by themselves--they are strong together. Also, if the AI is looking for mutual defense from a friend, maybe it will stick around longer.
Next, make sure the EU cities are completely developed and economically strong. Give the EU some attitude bonuses toward it's Vassals, and a sizeable headstart in culture. In time, cities may begin to culture-flip to the EU.
Finally, I do not understand how they AI works well enough to know if placement of Corporation HQ's and resources could also be used to hold the arrangement together.
Overall, it would be a way of simulating the EU as it works currently: a block of civ's combined to ensure mutual trade routes and mutual defense, and hopefully technology trading. Even the EU's military force can be explained in the European Security and Defence Policy.
Ideally at some point, through superior culture scores, the EU would absorb most of the cities leaving only the member civs' capitols. The alternatives would be a sort of civil war with the EU and it's Vassals retaking a member civ by force, or perhaps a member civ becoming strong enough to take over control from the EU. Besides those outcomes, there's always the obvious possibility that the EU could be picked apart by Russia, China, the USA, or some other civ.