Hi!
I know this question is old, but i wanted to write about the European Union because frankly it's the most underrated topic and noone ever cares about it neither in history or politics :(. Your question kind of misunderstands how the European Union got to where it is.
What is the European Union
Firstly, the founding of the European Union is not comparable to the US. The European Union was established with the Maastricht Treaty in 1993, after a gradual (with very varying speed) integration over about four decades. The modern treaty governing the EU, however, is the Lisbon Treaty of 2007 (specifically, the Treaty on European Union and Treaty on the functioning of the European Union. These treaties are also a mess and a mix of an intergovernmental organization, a supranational institution and a state - and are a result of compromises between the EU itself, state interests and the interests of civil society, rather than a deliberate and thought out goal.
I suspect what you are asking isn't the motivation behind these 1993 or 2007 treaties, but rather behind the initial concept of transnational European integration and possibly the European Steel and Coal Community (ECSC) of 1951.
Because of what the EU is, there is no one set of founding fathers for the EU, nor one inspiration. This makes analysing the EU a lot harder, and it's it's own branch of International relations and comparative politics. Contemporary scholarship tends to look at state interest, they tend to look at how integration typically spills over, and they tend to analyse the EU not just as a cooperation of states, but one or a set of independent actors with their own interests. Because integration was gradual, there is no "one" set of explanations or inspiration for how we get to the Lisbon Treaty of 2007.
HOWEVER, we can look at what inspired the initial start of the ECSC and the idea of European cooperation.
Historical background
The historical context is important. Germany and France had been at war three times in the last 80 years (Franco-Prussian war, First world war and second world war) and after WW2 there was a general trend of internationalism (which we had seen after WW1 as well, just stronger). Parts of this development was the UN, the European Court of Human Rights and the European Council and eventually the other human rights instruments, from the Bretton Woods conferance we got GATT, The IMF and the IBDR. In general - it was a time for internationalism. This was part of the general ideological context for the EU.
Furthermore, Europe specifically had three problems: (1) How to deal with Germany after 1945. How could one prevent the rise of a new strong germany seeking to dominate the continent; (2) The start of the cold war and a split Europe between the great powers, who were no longer west-european and; (3) How to rebuild a destroyed Europe and improve general welfare.
The idea of European cooperation was not new in the postwar, several thinkers and politicians had advocated for it at earlier times, even for a federation type of structure. This was semi-popular during the second world war, both among allies and axis. One of the key influential people at the time was former italian communist Alterio Spinelli, whose manifesto for a free and united Europe was widely circulated during the war, calling for a federated Europe and the world. And we can probably argue Spinelli was influenced by Trotskyist internationalism, but this is however not the case for any of the other "founding fathers" of the European union. And Trotsky (or lenin for that matter, or Marx) don't really have concrete ideas for how a state should look either.
But in the postwar there was really no climate or support for such radical proposals and national interests were strong and generally opposed, especially of course the likes of the UK. The general internationalist euphoria died down in the early 50s as well. Rather, french foreign minister Robert Schuman and his advisor Jean Monnet had a much more pragmatic approach to european cooperation.
The idea was to bind states together in a degree that would prevent future wars. But losing political sovereignty was controversial (a proposal on that failed in 1953), so they did not suggest a union. Rather, they suggested the fairly boring topics of coal and steel. Free trade and open markets weren't politically controversial, but these resources were central to warmaking so cross-border trade in them would make war economically harder. Part of the idea is that by integrating in the less controversial areas, that eventually spills over and makes cooperation in controversial political areas more possible.
Konrad Adenauer, german chancellor, saw european cooperation and unification as a way by which German self-respect could be regained and a way for Germany to reestablish itself in the international community, so the Germans supported the french proposals.
Even if the proposals were more modest, the goals of these politicians were were comparable to those who wanted a federation, like Spinelli. In his abovementioned manifesto he doesn't argue for a specific political system (compare that to The federalist papers for example), rather the system is the means by which one can avoid conflict and nationalism. This is also (at least partially) the goal here of Monnet, Schuman and Adenauer.
Here is a quote from the Schuman Declaration (1950)
Europe will not be made all at once, or according to a single plan. It will be built through concrete achievements which create a de facto solidarity. The coming together of the nations of Europe requires the elimination of the age-old opposition of France and Germany. Any action taken must in the first place concern these two countries
Conclusion
So the "founding fathers" of Europe had a very piecemeal and pragmatic approach, rooted in the post-war geostrategic and traumatic experience and in national interests. To answer your question specifically: No, there aren't any models or thinkers we can specifically point to. Europe is largely a product of specific post-war conditions, and gradually developing negotiations and cooperation over decades.
Of course the ideas of the general western tradition and values in the national systems have been influential for the EU, but unlike the founding of the US (or many other early national constitutions, like the Norwegian of 1814) the EU system was not founded at one place and time from a set of ideas, the EU institutions and systems weren't a goal in themselves, but rather a means to an end, continually created or changed to solve problems.
The 2007 Lisbon changes, for example, were largely ment to solve the problems of eastern expansion and structural problems with the earlier system, rather than adhere to some ideologic goal.
And the current European Union isn't really comparable to any other modern institution. It has it has taken elements from intergovernmental institutions, supranational institutions and from national states. Some comparisons have been drawn (by theorists, not the founding fathers) to various pre-modern medieval political institutions of mixed government, composed of several bodies with various authority and in some degree of competition, but i won't comment on how useful or accurate these are.
Sources:
Tömmel, Ingeborg (2014): The European Union - What it is and how it works London: Palgrave Macmillian
Nugent, Neill (2017) The Government and Politics of the European Union 8th ed. London: Palgrave Macmillian
Michalsen, Dag (2011) Rett - en internasjonal historie (Law - an international history) Oslo: pax
Heywood, Andrew (2013): Politics 4th ed. London: Palgrave Macmillian
Pevehouse & Goldstein (2017): International relations brief 7th ed. Boston: Pearson
Sejersted et al. (2011): EØS-Rett 3. utg (EEA-law 3rd ed.) Oslo: Universitetsforlaget
Schütze, Robert (2015): An introduction to European Law 2nd ed. Cambridge University Press