FOR once, Europe’s leaders seemed to agree: the European Union must change, and fast. After the European elections on May 22nd-25th, which saw the strong rise of radical parties of both the left and the right, the union had to do more to promote growth and jobs, and to become more relevant to citizens.

Such was the message issued by François Hollande, the French president, and David Cameron, Britain’s prime minister, both humiliated after their parties were trounced into third place by anti-EU parties of the right. The call was also echoed by Matteo Renzi, the Italian prime minister, who was boosted by the success of his Democratic Party in seeing off the challenge of the Five Star Movement. “We must change Europe to save it,” he declared.

Angela Merkel, the German chancellor, was quick to agree, even though she once more confirmed her talent for winning elections. The emergence of a tame Eurosceptic party, Alternative for Germany, which wants to abandon the euro but not the EU, was contained to 7% of the vote, a far cry from the roughly 25% secured by Marine Le Pen’s National Front in France and Nigel Farage’s United Kingdom Independence Party (UKIP) in Britain. Yet there is a sense of alarm in Germany about France. Germany had an “utmost interest” in helping France recover growth and competitiveness, said Mrs Merkel. Without that the euro zone could not be stabilised.

What will Europe’s leaders do to quell voters’ ugly mood? The quest for the new president of the European Commission is likely to turn into another messy wrangle (see Charlemagne). Its mandate to promote growth, competitiveness and jobs (in that order) is likely to be little more than a pastiche of fine words. And leaders disagree over how growth can be rekindled. As ever, the French want measures to protect industry, the British want more openness and competition, the Italians want a relaxation of fiscal rules and the Germans still see the problem in terms of export competitiveness (principally due to wages rising faster than productivity).

The European Parliament, hitherto a bastion of European federalism, is set to become the beachhead for all sorts of anti-Europeans. The most strident have roughly doubled to about 100 out of 751 seats. More broadly, anti-establishment parties control nearly one-third of the parliament. Beyond the victories of Eurosceptics in France and Britain, the anti-immigrant Danish People’s Party won in Denmark, the far-right Jobbik came second in Hungary and Germany has its first neo-Nazi MEP. The rise of insurgent parties is a sign of disillusion after years of economic crisis and of a longer-term fragmentation of traditional left-right politics. Yet, despite notable victories, radicals did not do well everywhere. The anti-immigrant Freedom Party of Geert Wilders lost support in the Netherlands, as did Finland’s Finns party. In the European Parliament the four main pro-EU groups still control about 70% of the seats compared with 80% in 2009. The centre-right European People’s Party and the centre-left Socialists & Democrats alliances will have to form a German-style grand coalition to pass laws. But this would only formalise current practice. About three-quarters of votes in the parliament are already carried with the support of both formations. Right-wing radicals have proved fractious, with a poor record of attendance. For the most part they have used the debating chamber as a giant YouTube channel. The myriad parties to the right of the EPP, ranging from Britain’s euro-reformist Tories to the far right, are jostling to form as many as three separate alliances. These bring the advantages of additional speaking time, committee positions and, crucially, public money. Groups must have at least 25 seats each and seven nationalities; the second condition is especially hard to meet.

Mr Farage refuses to form an alliance with Ms Le Pen, whom he regards as tainted by racism and anti-Semitism; Ms Le Pen feels similarly about Hungary’s Jobbik and Greece’s Golden Dawn. It is still possible that UKIP or the National Front will find themselves without sufficient allies.

Europhiles hope that a combination of economic recovery and firm leadership can still push back the wave of Euroscepticism. But the impact of the radicals will be felt in several ways. First, they will form a noisy opposition to initiatives by the European Commission. Second, and perhaps more importantly, they will affect domestic politics in their home countries, which will in turn constrain governments’ willingness to embark on risky European projects. As Mr Farage put it, European integration once seemed inevitable; now that sense of inevitability has gone.

One hopeful outcome will be to get the commission to streamline its work and reaffirm the doctrine of “subsidiarity”, whereby the EU should only do things that are demonstrably dealt with more efficiently at European level. Handled properly, a realignment of powers and priorities might provide an opening for Britain to renegotiate its relationship with the EU.

The global repercussions may be more worrying. The new European Parliament will probably be more sceptical of free markets and less favourable to free trade, particularly the ambitious Transatlantic Trade and Investment Partnership with America. One of Ms Le Pen’s demands is the immediate suspension of these negotiations. Moreover, anti-EU parties are often markedly pro-Russian. Internationally, the loser of these elections could be America—and the winner, Russia.