In France, politics is happening at a ferocious pace.

This country – big, wealthy, influential and vital to the stability of Europe – is suddenly facing a moment of tumult. Change, and perhaps really big change, is looming.

There are election posters up everywhere, candidates staring out at you with fixed grins and slogans. But there is one face that seems to appear more than anyone else – Marine Le Pen.

A fixture in French politics for a quarter of a century, she has stood for president, rebuilt her party, and even remoulded France’s far-right conversation. But now, more than ever, she sits on the brink of real power.

After Sunday’s election, the polls suggest that her far-right Rassemblement National (RN) will be the biggest winner, even allowing for the curious complexities of the French system.

A left-wing alliance will probably come second with the centre-ground party of President Emmanuel Macron trailing along in third.

If – and it’s a huge, wobbly, unreliable if – the RN were to get most seats in the National Assembly, the country would be transformed.

Madame Le Pen’s protege, the 28-year-old Jordan Bardella, would inevitably be installed as prime minister, working uneasily alongside a president who loathes pretty much everything that the RN stands for.

Mr Bardella would want much tougher laws against immigration, and against supporting immigrants.

He would also want to unwind some of Macron’s economic reforms and is much more sceptical about European integration than Macron.

How, you might wonder, could these two politicians work together in any meaningful way?

It would pave the way for instability, but also for the RN to flex real political clout.

And it would also lead to Ms Le Pen, once again, running for president. And as I write this, she is the favourite to win that contest, too.

But back to that big “if”.

France has a two-round voting system, with a week in between ballots. Candidates knocked out in the first round often advise their supporters who to back in the decisive second ballot. People might change their minds anyway.

The results from the first influence the way people behave in the second. A higher turnout may help the RN, except in the big cities, where it will probably help their opponents. It is a confusing, noisy mechanism almost everyone agrees on two things.

Firstly, the RN, led by Le Pen but also focused upon Mr Bardella, is destined to win more seats than any other party. And, secondly, this is all the more frenetic because it came out of the blue.

Make no mistake, a month ago, none of this was predicted. Sure, everyone knew that the Renaissance party of President Emmanuel Macron was likely to suffer a bloody nose during the European elections.

The RN, powered by disaffection with Macron and the populist, anti-immigration, “France First” rhetoric of Ms Le Pen and the youthful Mr Bardella, was certain to prosper.

But history is littered with mid-term elections that produce curious results. Macron, surely, would just shrug it off.

Except he didn’t.

Humbled by the scale of his defeat, Macron went on French television within minutes to announce that he was doing the very thing that his enemies in the RN had demanded – using his presidential power to dissolve parliament and call for fresh elections within weeks.

His logic was that the nation – his nation – would somehow come to its senses and turn its back on radical politics in general, and the RN in particular. And the evidence is that, fuelled by his own iron-clad self-belief, he got that wrong.

So what’s happening? More than anything, this is about two big political waves meeting each other. The first one has to do with Macron himself, whose popularity has simply declined. The second has to do with the ripple of populism that is moving through so many countries.

When he stormed to the presidency seven years ago, he was seen by many as the fresh new start that France needed – a dynamic young man, just 39 years old, who would shake up the nation and bring back some sense of dynamism and glory.

In the run-off against Ms Le Pen, he pitched himself as the politician of optimism, and her as a figure of hate. It worked – he won easily.

His follow-up victory a couple of years ago was less overwhelming but still comfortable. But then he lost control of the parliament and his control waned.

The old complaints came back – that he is, to quote an accusation I’ve heard countless times – the “president for the rich”; that he doesn’t understand the problems of normal people; that his interest is in promoting himself, not his country.

During the violent riots in Nanterre last year, Mr Macron’s government looked hopelessly leaden, while his efforts to raise the retirement age caused widespread fury.

His opponents from the centre have fragmented but his rivals on the left and right have become emboldened.

So while Mr Macron has tried to sound reasonable and emollient, he’s faced strident, unapologetic rhetoric from left and right, which has found an ever-greater audience.

Mr Macron is still a young man by the standards of global political leaders but perhaps his nation is now fed up with him, particularly at a time when so much space in the European political arena is being taken by leaders who favour strident opinions over considered nuance.

The French just have to look over their border with Italy, after all, to see how Giorgia Meloni’s brand of right-wing populism has prospered.

Look, perhaps, at the success in the Netherlands of Geert Wilders, a man who, like Ms Le Pen, spent decades in the political margins, confident that one day his time would come.

Or consider the volume of support given to the farmers who brought France’s motorways to a halt, angry with governments in Paris and Brussels.

The RN has tapped into that discontent and also benefited from it.

Sky News Data has analysed voting data from across France and drawn a few clear links that occur again and again.

In places where unemployment is high, such as near the border with Spain, or where disposable income is low, such as northwest France, the RN scores highly.

Madame Le Pen herself represents one of these places in the assembly – the 11th constituency of Pas-de-Calais. It includes Henin-Beaumont, a coal-mining town where she used to be a councillor and which is now an RN stronghold.

All around it are slag-heaps, now covered in grass. They are a reminder of the town’s past and also induce a widespread and lingering sense of resentment that the area, and its people, have been left behind.

If politics is a horseshoe, this is Mr Macron’s problem. The far-left leaders, like Jean-Luc Melenchon, condemn the President for not doing enough to protect workers and for damaging the fabric of society. So, too, do Ms Le Pen, Mr Bardella and the far-right.

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Their solutions are different, with Mr Melenchon’s rhetoric focusing on tax rises for the rich and stronger workers’ rights, while Ms Le Pen talks about immigration and protectionism, but perhaps the specifics don’t matter.

The fact is that after years of leadership from the centre, France is now increasingly looking to its margins.

We know the RN will do well, so the question is now just how well. And if they don’t take an absolute majority, and if Mr Macron resists appointing Mr Bardella as prime minister, what happens then?

Will the French government grind to a halt, gummed up by political divisions that stop anything being done?

Could Macron, as proud a leader as you’ll find, ever really be pushed into resignation?

We simply don’t know. And that is what makes this election so enthralling but also slightly unnerving.