It seems to me that the big problem with Europe us that nobody knows what they want Europe to be. On the one hand, nobody appears to want a loose association of sovereign states (like the original Common Market). On the other hand, Constitution or not, nobody appears to want a federal European State along the lines of the USA, with a strong Federal government. As soon as the EU starts to encroach on national sovereignty, cries of "Enough!/Assez!/Genüg!/etc., etc." are heard. Ultimately the pollies, no matter how pro-European (whatever that means), are voted into office by voters on a national basis with national concerns, and they can't ignore that (well, not all the time). As a result, we have this eternal fudge, major-league (and extremely well paid!) bureaucracy and complete confusion. Until they decide exactly what sort of Europe they want, and put that in clear terms to the national voters, they go nowhere. Can you imagine the board of a major company putting something like the EU Constitution to the shareholders at the AGM, unless the getaway car was round the back with the motor running?
Perhaps Switzerland is a good model. The country actually didn't become a Federal state until the late 1800s. Before that, it was a loose confederation of independent cantons. When a new canton joined, it signed an agreement with all the rest and then continued doing its own thing. The Sonderbund War in the 1840s (Switzerland's last war), when the Catholic cantons tried to secede and form a separate confederation, was a wake-up call to the fact that this old arrangement, which had endured nearly 600 years, was no longer appropriate. So the Swiss Confederation (still its official name) acquired a Federal constitution, with Bern as "Federal city" (some Swiss don't like the word "capital").
The individual cantons still retain a considerable degree of autonomy, more so than US states. For example, tax collection is done on a cantonal basis, and the canton then decides how much the Federal government deserves to get. The cantons and the Gemeinden (local councils) split the lion's share - 75%-80% - between them. My tax goes to the canton of Basel-Land, not Bern.
Similarly citizenship. My elder daughter is now a Swiss citizen. Who decides? Not Bern, not even the canton, it's the Gemeinde - they vote to see whether the applicant is worthy of becoming a citizen of the Gemeinde. If the vote is yes, the cantonal and federal authority rubber-stamp it. If the Gemeinde says no, only in exceptional circumstances can the other two step in. In the end, a Swiss is, first and foremost, a citizen of his or her Gemeinde, secondly a citizen of the canton and only thirdly a citizen of the political entity called the Swiss Confederation.
Switzerland is governed by a Bundesrat (Federal Council) of seven members ("the seven dwarves"). Bundesrat membership is allocated not only to the political parties in relation to their share of the vote, but also such that all the linguistic regions are fairly represented. This sort of consensus politics can mean that things can move pretty slowly, but it also makes sure that everyone gets a fair crack of the whip. And all issues of importance are put to a referendum.
A perfect system it is not, but it is an example of a system that works for a multilingual, multicultural entity. Perhaps it or a version of it, could work for Europe.