Your analogy is wrong. America is nothing like the EU. The EU is a league among sovereign nations with a procedure for leaving it. The constitution is fundamental law with no procedure for leaving.
You missed my point. America IS a league of sovereign nations. Massachusetts, Rhode Island, Connecticut, New York, Virginia, etc. WERE nations in precisely the same way that France, the UK, Germany , etc. are. Technically thats still true although our legal and political systems have evolved in a way that pretty much has rendered that status null and void. The states are the sovereign entities, not the FedGov. The states have voluntarily delegated some of their inherent powers as sovereign states to a central government. Havent you ever wondered why we have states rather than districts, provinces, departments, etc. as our subdivisions? The term state is synonymous with nation, France is a state. Belgium is a state. Technically Pennsylvania and Kentucky have the same political status as France and Belgium all are sovereign states. If a sovereign state agrees to voluntarily enter a league such as the EU, does it not have the right, by virtue of its sovereign status, to leave that league?
I understand that this conception of the US seems just wrong today. It IS wrong based on how our political system has evolved. The point is that in 1860 this conception was 100% accurate. The FedGov played very little role in most peoples lives. (Mail delivery was about the only thing most people would have seen from the Feds). Even armed forces, while authorized by the Feds were mostly recruited and governed at the state level. When Lincoln called for troops to put down the rebellion, STATES actually raised the troops. A person volunteering for service did not enroll in the US Army, as he would today. He enrolled in a state regiment, which was subsequently sent to the battlefield and integrated into a brigade in the larger army. If you had a time machine and asked a Civil War soldier where he was from, hed never say America or the Confederacy. Hed tell you what state he was from.
In much the same way, its highly doubtful that if you asked a random person in Paris where hes from that hed say Europe or the EU. Hed say France. Who knows what will happen? Maybe 150 years from now the idea that France, Germany, etc. were independent governments at one time will seem just as incomprehensible to people as the notion that Virginia and South Carolina once were independent nations. That was the original concept of our Constitution though. States were to maintain their sovereign status and voluntarily delegate some powers to a central government. The fact that weve lost that concept doesnt change anything. That was in fact one of the two fundamental changes caused by the war (the other obviously being abolition of slavery). Before the war, the US was not really a nation, but something very much like the modern EU.
The procedure for leaving was explained in the Declaration of Independence, which *IS* the founding document of this nation. The US Constitution is the second addendum to it.