France’s own economic problems will soon make it unable to help bail out weaker European countries. When that happens, the euro game will be up

Chris Ratcliffe / Bloomberg via Getty Images Shares of Société Générale, a major French bank, have lost half their value since March

Last week’s deal to save the euro has contained the problems in Greece — at least for the moment. Now all eyes are turning to Italy as the next potential crisis hot spot. But there’s no need to go through the troubled economies of Europe one by one, trying to assess their individual prospects. In the end, there’s only one country that matters. The survival of the euro currency — and the entire European economic system that goes with it — ultimately depends on France.

Even in the short run, the deal announced on Oct. 27 in Brussels hardly seems worth cheering about. European leaders agreed to increase the size of the bailout fund. Banks will boost their capital, but they will largely have to raise the additional money on their own. Many private-sector holders of Greek debt will have to accept a 50% loss on the bonds they own. Expert observers say the terms are hard to evaluate, and some think the deal will fail within a matter of weeks.

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Nonetheless, stocks rallied powerfully toward the end of last week. In fact, with a 14% gain for the S&P 500, October has been the best month for U.S. stocks since 1974. That shows two things. First, stocks are cheap enough from a long-term perspective that they will rally on any improvement in short-term global financial problems. Second, the markets were afraid of a much-worse outcome from the Brussels meeting. Stocks rallied not so much because the agreement solved the problem, but rather because the day of reckoning was postponed once again.

But even if Greece has been dealt with successfully, there are more serious problems spread throughout the European economic system. Attention seems to be turning to Italy as the next weakest link in the chain. That country’s debt is huge, and tens of billions of dollars have to be rolled over within the next six months. The most ominous signs come from the financial markets themselves. Italy’s borrowing costs have actually risen since the Brussels agreement was announced. And European banks continue to have trouble obtaining adequate funding. Both are clear signs that investors don’t believe Europe’s financial problems have been fundamentally resolved.

Ultimately, however, the question of the euro and the European financial system comes to rest with France. The whole process of containing the problems of weak European economies depends on having enough financially strong countries to pay for the bailouts. And equally important, there has to be a widely held belief in common European interests. France is essential to both those things.

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It’s increasingly clear that Europe is developing into two economic blocs with diverging destinies. On one side is Germany and some smaller countries — such as the Netherlands, Austria and Finland — that have similarly strong economies. On the other side are Greece, Spain, Italy and all the other countries facing severe debt problems.

The wealthier countries see less and less reason to keep paying for bailouts. Most have growing right-wing movements opposed to subsidizing the poorer countries in the euro-currency zone. And even among more mainstream political parties in Germany, Austria, the Netherlands and Finland, there is skepticism about the euro. What keeps them engaged is the perception that there is a broad European constituency for the common currency. And that broad constituency is largely built around the partnership between France and Germany, on which the entire European Union was founded.

Soon, however, France’s problems are likely to begin absorbing all its economic resources. While many European banks are exposed to potential losses on Greek and possibly Italian debt, French banks are among the most vulnerable. As a result, shares of Société Générale, BNP Paribas and Crédit Agricole have all lost almost half their value since March. France’s AAA credit rating has been at risk for several months. Two weeks ago, credit-rating agency Moody’s warned of a possible downgrade for France. And although President Sarkozy has declared that he will do whatever it takes to defend the credit rating, the austerity required will be politically difficult, especially in light of France’s presidential election next year.

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Remove France from the group of countries that can afford to pay for bailouts and you have just a handful left. Not only will the remaining rich countries feel the loss of France’s financial contributions; they will also lose much of the psychological motivation to defend a common European currency.

Without the French-German axis, there remains only a small group of northern countries linked to Germany that would perhaps be better off separating financially from the rest of Europe. Some political and business leaders in those countries have already called for such a move. And from a purely economic point of view, such secession makes sense.

What prevents it is the argument that Europe is somehow bigger than just economic calculations. That larger vision depends on France’s remaining capable of playing a leading role. No matter what happens elsewhere, if France’s financial problems remove the country from the equation, there will be just a group of northern countries picking up the check for everyone else. And there’s no practical reason for them to keep doing so for very long.