France has held its second round of regional elections, with Marine Le Pen's far-right National Rally (RN) again failing to take power anywhere.

It had hoped Provence-Alpes-Côte d'Azur would be its first regional victory but it was won by centre-right Republicans.

They and the Socialist Party both received surprise boosts in polls that favoured the incumbents but drew a meagre turnout of under 35%.

President Emmanuel Macron's party suffered more bad results.

His centrist La République En Marche (LREM) also failed to win control of any region.

It also performed badly in the first round, which was held last week.

It was the first time President Macron's party had taken part in regional elections, as it did not exist the last time they were held in 2015.

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Ms Le Pen sought to win one of France's mainland regions for the first time in a bid to boost her presidential election hopes in 2022.

But in Provence, the hotly tipped RN candidate, Thierry Mariani, lost to Republican Renaud Muselier.

"Tonight we have chosen the fate of a free region," Mr Muselier tweeted. Left-wing candidates withdrew from the race in the region to help the Republican defeat Mr Mariani.

Ms Le Pen accused her rivals of forming "unnatural alliances" to block her and her party from power.

"[They] did all they could to keep us out and prevent us from showing the French our capacity to lead a regional administration," she told supporters.

The Hauts-de-France region around Calais in the north had also been earmarked as a potential gain for Ms Le Pen's RN, but was won by conservative Xavier Bertrand.

"The far-right has been stopped in its tracks and we have pushed it back sharply," he told his supporters after the polls closed.

All of the incumbent regional presidents who ran again, whether left or right, were winners.

A big disappointment for Le Pen
Analysis box by Hugh Schofield, Paris correspondent

President Macron's party was already sidelined in these elections after its poor showing in the first round.

Marine Le Pen's also scored badly last Sunday, but she at least had hopes of picking up one region - which would have been a first and a boost for her presidential bid.

It didn't happen - once again her voters stayed away from the polls - and overall these elections have been a big disappointment for the hard right.

The winners are the mainstream right whose candidates held on easily to the regions they already controlled. One of them the former minister Xavier Bertrand, whose fief is the northern Hauts-de-France region, is now openly a candidate for the presidency next year.