Habsbourghs always wanted to rule all of Europe, but the pesky nationalists and republicans prevented them from achieving their goal they once almost had. Archuke Ferdinand's plan was to reform Austria-Hungary (which itself was attempt to reform feudal monarchy into nationalistic state that failed spectacularly) into United States of Europe, but I don't need to explain what prevented this goal of his.
They realized they need to get rid off nationalists. For this reason, they are the chief supporters of the Pan-European society.
You might have heard about Kalergi's plan.The founder of Pan-European society was no other than count von Kalergi.
Pan-European movement was then the ideological basis for EU and European People's Party in particular (the party coglomerate that rules the European Parliament)
The President of the movement for 40 years was Otto von Habsbourgh, the crown prince of Austria, also Austrian Volkpartai member (which itself is the member of the EPP).
These people are also behind the Pan-European Picnic (1989) which is an event that sparked the Berlin wall downfall. The speaker at that even was again, the president-king Otto.