If Mr. Hollande called a referendum, Marine Le Pen of the National Front would have a fantastic platform to rail against the loss of French sovereignty. Even the Italians are becoming euro-skeptic: Beppe Grillo, leader of the Five Star Movement, the country’s second most popular party, has called for Italy to abandon the euro, describing it as an “antidemocratic straitjacket.”

Doesn’t this then mean the eurozone is doomed? If 19 countries share the same currency and lose the ability to devalue when they hit problems, surely they also need a common treasury to cushion the blow? And then they need a common government and parliament to give legitimacy to their actions, right?

Not so fast. The crisis of recent years has two main causes: lack of competitiveness and excessive government borrowing. There are better ways to address problems of competitiveness than by agreeing on a treaty to mandate it; and we have already seen that treaties requiring fiscal rectitude have been pretty useless.

To lift competitiveness, the eurozone needs to free up markets. This will also allow the bloc’s economies to adjust more rapidly to shocks rather than millions of people being turfed out of work.

To be fair, the five presidents acknowledge this. Action is needed at a pan-European level to complete the single market in services, the Internet and energy. Creating a capital-markets union would soften the blow when a national economy suffered a downturn by spreading the pain across Europe.

The presidents also rightly call for more efficient national labor and product markets. They want each country to set up an independent competitiveness authority to drive this forward.

While this may be a good idea, the presidents are wrong to suggest that common standards for competitiveness should be hard-wired into laws applying to all 19 countries. This looks like a recipe for rigidity that will hamper innovation.