A week of campaigning and deal-making is beginning in France, ahead of a second round of parliamentary elections next weekend. It comes after the Far-Right National Rally Party emerged from Sunday's first round in a comfortable first place, with just over 33% of the vote. President Macron, whose alliance trailed in third place on around 20%, has responded by calling for centrists and left-wing parties to unite to prevent the Far-Right from winning control of Parliament. From Paris, here's Harding.

A dramatic win yesterday for France's National Rally. The party was, for years, considered too extreme for most French voters, with its anti-immigration, Euro-skeptic platform, and its links to the Kremlin. But last night, the RN, as it's known here, secured more than a third of all votes. The party's leader is Marine Le Pen, who has her eye on winning the French presidency next. Les. She told the country it had nothing to fear from a right-wing, RN-led government. But there is a second round of voting here next weekend, and things could still change. After yesterday's vote, President Emmanuel Macron called for centrist and left wing parties to form a united front to keep the RN out of power. Will it work? It's going to be a struggle. And all this in the middle of Paris's preparations for the Olympic Games later this month. Many French are worried about their country's deep political polarization. The road ahead will become clearer in a week's time when a second round of voting will determine France's future. That could be months of political deadlock. It could be a seismic political shift to the hard right, with huge implications for the country country and the continent.

Andrew Harding, BBC News, Paris.

Well, let's speak to our Paris correspondence, Huw Scofield. And Huw, in previous elections, the left and the center have come together to stop the far right from taking power in France, how successful will they be this time around?

We'll have to see. They're certainly making the same noises this time around. You heard Macron there calling for a front to confront and take on and defeat the RN candidates in each of their constituencies where they're through to the second round. So yes, and there is certainly a determination on the part of the left to do this. They promised that their candidates will stand down if they're in third place in a constituency in order to concentrate the vote against the RN candidate. It could make a big difference. The left did very well in this election. They got 28% of the vote. Their forces are traditionally very very fired up against the national rally. If there is a big turnout by people voting on the center and the left to stop the national rally, that could well limit the extent of their gains in this election. But gains there will certainly be for the RN in this election. The key question really is not if they win, but by how much. If they can't get this point of 289 seats, that's an absolute majority in Parliament, they'll be left incapable of governing, and then we are really in unknown territory.

Here, where does this all leave President Macron because this was a huge gamble for him to call for this Snap election.

Enfeebled, solitary, isolated, embarrassed, all those things. You're right, he promised to return France to the center, to form of bastion against the extremes of far-right and far-left. What's happened is that the country has become polarized. We have a far-right that is not far from gaining power and a left coalition which is dominated by the far left party, the LFI. So whatever it is that he planned to do, it hasn't happened. And the immediate prospect for France is one in which he himself is a very diminished figure with very little influence inside the country and a diminished profile outside the country. And inside the country, we have a far right, which may well form the next government, or a deadlock in Parliament, leading to, well, more crisis.

Yes, and you mentioned there the polarization within French society between the far right and the far left. How has this come about?

Well, partly it's because of what Macron has done. Macron posed and produced himself or represented himself as being the great center, the hyper center, the man who would unite France because around him would come sensible men and women of the center the centre-left and the centre-right, and that would be the obvious and logical solution to the country's problems. The only thing was that in the natural course of events, there was going to be an opposition to that. As he hogged the centre-ground, the opposition inevitably has come from what he calls the extremes, the extreme right and the extreme left. And that's what's happened. But of course, it's replicated in other countries. It's a polarization that's also cultural, linked to the rise of a left liberal, Metropolitan class, and it's a rejection by, for the bluntly poor white people living in the provinces.

And if, as expected, Hugh, the National Rally does form the next government in France, what policies could it introduce? Would it be very different from President Macron's party?

Well, first of all, let me just qualify that. We can't assume there will be a National Rally government after next Sunday. If they don't get this total majority, they will be incapable of forming a government. There's a lot of talk of them forming, there be some technocratic government, like what Italy had with Draghi. So let's not assume that the national rally are going to bring in a form in the next government. But if they do, well, we know what their policies are. They are to make immigration more difficult, to make life less attractive for people who would like to come and settle here. It's to make handouts, state benefits available primarily for people of French nationality. On the social-economic front, it's to increase people's buying power by cutting the AT on fuel and things like that, things that are going to cost an awful lot of money, reducing again the age of retirement. Whether or not in practice these things are practical is another matter, but that's what's on their manifesto.

Thank you very much, Huw. That's the BBC's Huw Schroeffield in Paris there.