EU leaders will this week debate proposals for closer unity between the euro countries, as they seek a way out of the crisis. But could greater integration be what finally blows the eurozone apart?

If you thought the Greek or Spanish crises were bad enough in the eurozone, imagine this: a eurozone split so fundamentally in the future that Germany and France end up on different sides - and a dispute about saving the single currency that leads to rows about, say, whether France can keep nuclear weapons.

It is a scenario European leaders would, in public at least, reject as ludicrous. The partnership between France and Germany has been at Europe's heart. Preventing conflict between the two countries was why European integration began after World War II.

But listen to top Harvard political scientist Dani Rodrik who thinks that, five years down the road, the eurozone will have shrunk to a core group centred on Germany, with a "50% chance that France will remain in".

And David Marsh, historian of the euro and co-chair of a group linking central bankers and financial organisations, says the battle over the single currency "will be joined across the Rhine. Which way the French decide to go, which way the Germans decide to go I do not know."

Is France allowed to have a nuclear bomb which costs I don't know how many millions… and then have a budget deficit?" Ulrike Guerot, European Council on Foreign Relations

So how could such a split come about?

It is all linked, paradoxically, to the way in which the European leaders may try to solve the current euro crisis, with a major leap towards closer economic and political union.

On the table at a two-day EU summit in Brussels is a plan for a European treasury with powers over national budgets.

As financial markets exert their pressure, and populations stuck in austerity become more desperate, all agree that change is needed.

Lord Mandelson, former EU commissioner and leading British supporter of the euro, told me: "I don't think the eurozone as currently constructed and designed, plus its existing members are compatible… Either its members have to change or the way it operates."

All eyes are on Germany, the largest contributor to eurozone financial firepower - and the country whose backing is crucial to a credible future for the single currency.

German Chancellor Angela Merkel has said that her country is committed to keeping the eurozone intact. To that end, the eurozone is inching towards a closer fiscal union, with shared responsibility for eurozone countries' debts.

But Germany will insist on a tough bargain - one with major political consequences which France, among others, might find impossible to accept.

Rule-breakers lose sovereignty "In the event of a country not abiding by the budgetary rules, national sovereignty would be automatically transferred to the European level on a scale that can ensure compliance with the objectives. "In a speech at the Petersen Institute, Jean-Claude Trichet, the former President of the ECB, described this aptly as 'federalism by exception'. "One option, for example, could be the right to make tax increases or proportional cuts in expenditure - and not just the possibility of calling for them. "In effect, national sovereignty would be largely retained and fiscal policy decision-making capabilities and room for manoeuvre would be preserved as long as a country in question complies with the limits on borrowing and debt." Read Jens Weidmann's full speech

The president of the German Bundesbank, Jens Weidmann - a former economic adviser to Chancellor Merkel, and an increasingly influential player in the eurozone crisis - has been indicating the kind of bargain Germany would demand.

He articulates what many Germans regard as essential if any deal is to be done and in a speech this month Dr Weidmann spelled out what would happen to countries in the new eurozone who didn't play by its rules.

"In the event of a country not abiding by the budgetary rules," he said, "national sovereignty would be automatically transferred to the European level on a scale that can ensure compliance with the objectives."

That European authority, he added, could have "the right to make tax increases or proportional cuts in expenditure", in a country affected.

Ulrike Guerot, based in Berlin for the European Council on Foreign Relations, says: "From a German perspective, eurobonds are not for free and this is what the other countries need to get."

Essentially, the price of debt-sharing through deeper economic union is loss of national economic sovereignty.

"I mean, is France then allowed to have a nuclear bomb which costs I don't know how many millions… and then have a budget deficit?" asks Guerot.

And this is when you realise the political implications of what may be happening as governments promise to unite further to save the euro. A new world in which other countries, led by Germany, question France's right to nuclear weapons.

Image caption Some people believe Germany already has too much control in the eurozone

But in a Europe becoming, in many ways, increasingly nationalistic and eurosceptic, as election results in Greece, France and the Netherlands demonstrate, that is hardly likely to win easy acceptance. German and French leaders will continue to insist that theirs is the key European partnership.

But historian David Marsh believes "the forces of history are probably moving away from the Franco-German alliance", with Germany placing increasing emphasis on new economic interests to the east, ranging from central Europe to Russia to China.

And personal relations between Chancellor Merkel and the new French President Francois Hollande are far from warm - she offered to campaign for Nicolas Sarkozy in the French presidential elections.

After Hollande was elected, his spokesman Benoit Hamon warned Berlin in a recent French TV interview: "We didn't have an election to get a European president called Mrs Merkel who has the power to decide everyone else's fate."

Imagine, then, the French response to that German idea of countries failing to follow strict spending rules handing over their national sovereignty.

And Hollande has a very different vision of how the eurozone should evolve - keen on seeing it as a club that, with the help of France's political leadership, sustains the financing of European growth.

So, while European leaders stress their determination to move towards a new kind of union to save the single currency, that only begins what will be the toughest of political as well as economic struggles.

"Over a three- to five-year time frame," argues David Marsh, "we will see this reduced to a Germanic core and we will have to ask ourselves whether France will be part of that core."

Unthinkable? Yes, many in Europe will say. The eurozone, just like the European Union, will muddle through this crisis, and a more united continent will eventually emerge.

But until a few months ago, the unchallenged orthodoxy was that the euro was irreversible - it was simply inconceivable and impossible for anyone to leave. Few say that now.

The challenge now, says Lord Mandelson, is "complete the project or sit back and watch it fail further".

"If the eurozone fell apart," he warns, "the human and social costs of the economic chaos… would be colossal."

But in trying to fix the currency crisis, could Europe be risking a split at the heart of European integration itself?

Listen to the full report on Analysis on BBC Radio 4 on Sunday, 1 July at 21:30 BST.

You can also listen again on the Radio 4 website or by downloading the Analysis podcast.