It is the biggest electoral contest in Europe, but frequently leaves many voters indifferent. Turnout in European parliament elections has been declining ever since the first votes in 1979.

Could this time be different? The next European elections will take place in May 2019, less than two months after Brexit day, and never before have the elections been labelled so decisive by so many European leaders.

During his successful run for the French presidency, Emmanuel Macron cast himself as the leader of the anti-populist, pro-EU forces. His opponents are eager to join the battle. Matteo Salvini, Italy’s deputy prime minister and leader of the anti-EU League party, declared (paywall) that the elections would be “a referendum between the Europe of the elites, of banks, of finance, of immigration and precarious work” versus “the Europe of people and labour”.

Hungary’s nationalist prime minister, Viktor Orbán, has said the vote will be a chance to say goodbye “not simply to liberal democracy … but to the 1968 elite”.

Parties such as Salvini’s League, Alternative für Deutschland in Germany and Marine Le Pen’s National Rally are expected to do well. A recent poll showed that the National Rally, formerly the National Front, had edged ahead of Macron, with 21% support, ahead of 19% for the president’s party, La République en Marche.

Support is growing in France for Marine Le Pen’s right-wing populist National Rally party. Photograph: Ian Langsdon/EPA

In Brussels, three scenarios have been floated: a decisive surge for anti-EU parties, unexpected gains for pro-European parties and a third option of something confusing between the two. “A mess is the most likely outcome,” said one senior EU source defining this as a “grey” outcome of “progress by the populists, but still a strong majority of 400 pro-EU MEPs”.

This “mess” is likely to spell the end of the grand coalition – the two large blocs representing centre-right and centre-left, which dominate the parliament and currently hold 54% of the assembly’s 751 seats.

The centre-right European People’s party has been weakening, a result of poor performances in several countries (including France), but also splits over how to handle its Hungarian member, as the country goes backwards on democratic freedoms.

Meanwhile the centre-left Socialists and Democrats party is expected to lose seats, as its member parties continue to fare poorly across much of Europe. The S&D faction will also be hit hard by the loss of 20 Labour MEPs when the UK leaves the EU.

The fall of the grand coalition will make the next European parliament more complex, with increased horse-trading and, possibly, as many as four parties needed to pass a law. Analysts writing for Carnegie Europe suggest it will resemble the Danish or Dutch parliaments, with more parties and more coalition options.

“There is a high risk of paralysis,” said Heather Grabbe, the director of the Open Society European Policy Institute and one of the co-authors. “As more challenges come up for the European Union, it could be impossible to get legislation through the parliament. It becomes therefore harder to work through the community method [of EU lawmaking] and that is going to have a big impact.”

European elections not only determine the makeup of the parliament, one of the EU’s two “co-legislators” along with the powerful EU council of ministers. The results also help determine the division of the EU’s top jobs. In 2019, the presidencies of the European commission and European council will both be up for grabs.

European elections – in reality a series of national elections – test the temperature of domestic politics. “Many use the European elections to show a yellow or a red card to the government,” says Janis Emmanouilidis, director of studies at the European Policy Centre. He thinks gains for anti-EU parties would “create pressures at the national level” meaning that the EU’s divided 27 governments are even less likely to agree on the fraught issues of eurozone reform or migration.

Both the future of the euro and migration are likely to be centre-stage during the campaign. Some suggest that framing the elections as a stark choice between the EU and anti-EU is problematic. Not only does it paper over the big differences among “pro-EU” parties, it also risks fuelling myths about what the EU does.

If the rules of the debate are set by anti-EU populists “who don’t really argue about what the EU is actually doing” but set up “straw man” arguments, that could rebound badly, said Grabbe. “It is quite dangerous because people will end up blaming the EU for all sorts of things it is not responsible for, rather than discussing its real powers and the things that really matter.”