It should have been the perfect entrée. On Thursday, Brian Cowen will meet his European counterparts for the first time at a meeting of EU heads of state at the Justus Lipsius with him, it would have been smiles all round. Nicolas Sarkozy, the French president, would have been beaming.

This week’s summit was to have been a pleasant two-day summer get-together, with talks about who might take the roles of the EU president and foreign minister — positions created by the Lisbon treaty. There might even have been negotiations about the creation of an EU diplomatic service.

Now the taoiseach faces a hostile interrogation instead. Where did it all go wrong? What’s he going to do about it? Europhile foreign leaders, fearful that Ireland’s No vote might set off a domino effect, will demand that Cowen provide not just explanations but a solution too.

The French are particularly horrified by the Irish vote. It has cast a shadow of uncertainty over their six-month presidency of the EU, which starts on July 1. Sarkozy had been expected to use his elevated status as president of the council to announce ambitious EU defence projects, and to arrange for suitable people to fill the new European roles. All that is now in doubt.

France has stayed fairly quiet about its ambitions for European defence, although some tantalising details have been disclosed. It was told to delay an announcement until after the Irish referendum, so as not to frighten off Yes voters who were squeamish about Irish neutrality. So will they risk announcing anything now?

No wonder Jean-Pierre Jouyet, the French secretary of state for European affairs, first said he was shattered by the No vote. On reflection, a few hours later, he was describing it as nothing more than an incident. “Europe has not broken down,” Jouyet said. “Nor is it in crisis. We are sad. We are above all sad for our Irish friends. But we must go forward.”

The sadness and regret about Ireland’s No vote struck a much different note to the talk of political “catastrophe” and “paralysis” that followed the rejection of the EU constitution by France and the Netherlands in 2005. Behind the scenes there was little official sympathy for Ireland — which is widely regarded as being ungrateful after pocketing so much European aid down the years.

There were suggestions that the Irish rejection of the treaty was less important than the French one, which was supposedly based on more high-minded reasons such as the retention of the country’s social model. “The Irish No is a liberal, reactionary and isolationist ‘no’,” said a writer in the left-wing Libération newspaper.

Jouyet said another “legal arrangement” with Ireland would have to be found. “There are always possibilities to find specific methods of co-operating,” he said.

Many European commentators speculated that France and Germany might have already plotted a plan C. Jean-Claude Juncker, the prime minister of Luxembourg, told German radio that the Irish rejection showed it was time to press on with a “club of the few” countries — those most enthusiastic about closer EU integration.

The Süeddeutsche Zeitung newspaper in Germany also suggested that the Irish vote could lead to a “two-speed Europe” with a handful of staunchly Europhile countries developing common policies of their own. The country’s foreign minister, Frank-Walter Steinmeier, told reporters during a trip to China that the onus was on Ireland to “clear the way” for the EU’s other 26 members to continue developing joint EU policies.

The British government is putting pressure on Ireland. Jim Murphy, the Europe minister, said it was up to Cowen to devise a way forward.