At the time the American Constitution was written, were the founding fathers hoping for a European Union style government or more of a statehood type of unity?

What they had in 1787 under the Articles of Confederation was more like the EU. The 13 colonies were in many ways their own little countries. They had their own currencies. They had some of their own diplomacy ( when John Adams was trying to borrow money in the Netherlands for the Revolution on behalf of the Continental Congress, he found that Massachusetts had already had someone there doing the same). They had their own militias. The Continental Congress could not tax, could not raise an army, didn't print money( the Continental "currency" -actually a promissory note- it issued during the War was regarded as valueless and unredeemable) and it could not really conduct foreign diplomacy.

This was not working very well. Now, just how well it was working and how well they hoped it all could work has long been a matter of debate among historians, and it's had political overtones. In the 19th c. the most common verdict was the Federalist one- the country had been in crisis, the economy was in ruins, armed insurrection threatened public order ( Shay's Rebellion) with no standing army to quell it, merchants couldn't do business because the colonies couldn't settle their foreign debts- and then wise men like Hamilton created the More Perfect Union which saved everything and life was good. And, there's no doubt good stuff did happen- it was much easier to settle the war debts, conduct foreign diplomacy, mount a response to an armed insurrection ( the Whiskey Rebellion) improve and manage interstate commerce, settle interstate legal disputes, have patent laws.

But in the 20th c. that nice, neat little story began to get questioned. Historians like Merrill Jensen began to wonder if the federal constitution had indeed been so inevitable. There was a pretty common 19th c. bias towards Whig History, which always presumed that humans were moving towards enlightenment and liberal democracy. In other words, there was a conviction that just because the constitution was created, it was naturally a step towards progress. Jensen and others thought that this was far too simple. They pointed out that the years 1782-1787 had not been necessarily ones of crisis. The states had some challenges and problems, true, but were still muddling along. Shay's Rebellion was a flash in the pan, an isolated incident.

The Constitutional Convention was also not unanimous. There were anti-Federalists in the 1787 Convention, and they also argued against the ratification afterwards. Some vry important people were anti- Federalists, like George Clinton, who had climbed high in local politics and was leery of losing some power. Some, like Patrick Henry, of Virginia, thought a President would just tend to become King. What if they had won, gotten more than just the Bill of Rights, and the 1787 Convention had come up with a document far more limited? That's presented a problem for historians. First, there are now political groups who would like to think it would have been just great to have a Continental Congress still, and historians don't really like getting squeezed to supply over-simplified hypothetical material for political talking points. Second, we don't know, really, what would have happened if the 1787 had done something far more limiting. To say what would have happened is playing a counterfactual game, and those games are , like I said, hypothetical. BUT one rather obvious hypothetical but inescapable issue for any confederation or union of the states would have been slavery. Abolition of slavery was not accomplished in 1787 and would become an insoluble problem , the main divisive issue for the Republic, culminating in a Civil War, giving the nation problems that still exist. It's hard to see how a weakly-binding EU-like structure would have ever abolished it, how it would have been ended without a pretty solid constitution binding the states together.