It turns out that the widespread predictions of a far-right takeover of the European parliament were, as Mark Twain famously said about reports of his death, “greatly exaggerated”. Citizens across Europe flocked to the ballot box in numbers unseen since the 1990s. The young in particular turned out. And they did not deliver a rightwing populist surge.

A political shift is undoubtedly under way and rightwing populism is still very much around. But the real story was the evidence of a new pluralism emerging in EU politics, including a Green and liberal surge. None of this imperils the EU’s survival; quite the contrary. Nor will it lead to a paralysis of its institutions, although coalition-building will be trickier than before. Given the doomsday scenarios doing the rounds, this is good news.

When EU leaders meet on Tuesday to take stock of these results, they will reflect on how a bloc of 510 million people in the end pulled itself back from the brink. The EU as an entity has been routinely depicted as on the verge of self-destruction. At the height of the refugee crisis, and following Brexit, Cassandras were everywhere. These elections have also delivered a rebuff to the likes of Donald Trump, who has described the EU as a “foe” and has actively encouraged its breakup. The same goes for Vladimir Putin, who has predicted that the bloc will eventually implode as a result of western “decadence” (a favourite Putin slogan).

Marine Le Pen’s National Rally led the polls in France, but it should be remembered that her party also came first in the 2014 European elections: the far right has essentially cemented its position in France, not surged to new heights. It’s also worth noting that Emmanuel Macron’s Renaissance list,though it came second on 22.4%, did hold its ground on Sunday by coming close to Macron’s personal score in the first round of the French presidential election. Given that the past seven months in France have been dominated by the chaos of the “gilets jaunes” crisis, that amounts to reasonable damage limitation for Macron, not a wipe-out.

That Matteo Salvini’s League leads in Italy is of course a source of concern – the first time the far right has come out on top in an Italian election. But that outcome was predictable. The more surprising development in Italy was the revival of the centre-left Democratic party, which easily outscored the League’s coalition partners, the Five Star Movement.

In Germany, France and elsewhere, a good night for the Greens indicated the rising priority of environmental issues for European voters. It also suggested an awareness that the EU as a bloc, not the individual nation-state, is the best level for effective action to tackle the climate crisis.

More seats in the European parliament will be handed to far-right groups and their potential allies (which have sometimes included the far left, as when they rejected a resolution calling for the release of political prisoners in Russia last year). But more importantly these election results have newly empowered centrist forces – the ALDE (liberal) and Green groups are now potential kingmakers in Strasbourg. Meanwhile the far left didn’t do well at all, in particular in Greece and France.

For the traditional European powerhouses (the mainstream right and the social democrats), this was a difficult night. Both suffered losses, reflecting the domestic pattern in many countries. But even here we should be careful: in Germany the party of a chancellor who’s been in power for nearly 14 years still managed to lead the second-placed Greens by 8%. Given that her handling of the refugee crisis was supposed to have so damaged Angela Merkel, this hardly amounted to humiliation.

Europe is a complex place, a patchwork of 28 domestic political scenes, and we must avoid the temptation to over-generalise. There can be a sigh of relief that the far-right in Germany (AfD) and in Spain (Vox) did less well than in other, recent votes in those countries. But France is much less reassuring, and Macron will continue to have a hard time delivering on his EU-wide ambitions.

Similarly, to speak of the death of social democracy by a thousand cuts may ring true for the German SPD or the French Socialists; but the picture is entirely different in the Netherlands and Spain, where a young Socialist prime minister has found ways to raise the minimum wage and promote gender equality.

Hungary’s Viktor Orbán – who, don’t forget, controls most of the media in his country – can yet again claim a victory, but hasty narratives about central Europe becoming a monolithic centre of rightwing populism will have been dented by these results. The pro-European opposition in Poland now believes it has a fighting chance in the general election due later this year. Meanwhile Slovaks and Romanians (especially expats living across the EU) have delivered a blow to the corrupt power networks that run much of their national governments.

It is too early to say how successfully Europe’s far right will manage to coalesce into a single bloc in the EU parliament. But there is also more for progressives to be optimistic about from these results than anyone had expected: many citizens have mobilised against the dark forces of rightwing populism. For European citizens, some fundamental values and achievements turned out to be worth cherishing, not throwing away in a fit of anger. Perhaps there is more common sense and moderation than we feared in Europe’s political landscape. The centre is holding.

• Natalie Nougayrède is a Guardian columnist