French voters are being courted across the spectrum for a run-off election after shutting out the country's political mainstream from the presidency for the first time in the country's modern history.

Police said six officers and three demonstrators were injured in election night violence on Sunday in which protesters burned cars, danced around bonfires and dodged riot police.

They said they had detained 29 people in the unrest between protesters and police at the Place de la Bastille in Paris.

Protesters waved red flags and sang "No Marine and No Macron!" in anger at the results of the first-round election.

Some 300 people gathered at a peaceful protest at nearby Place de la Republique, waving red flags and dancing around the flames of a bonfire.

Some sang "Now burn your electoral cards" or "No Marine and No Macron!".

The Herald:

The May 7 run-off will be between the populist Marine Le Pen and centrist Emmanuel Macron, and French politicians on the moderate left and right immediately urged voters to block Le Pen's path to power.

The defeated far-left candidate, Jean-Luc Melenchon, pointedly refused to do the same, and Le Pen's National Front is hoping to do the once unthinkable and peel away voters historically opposed to a party long tainted by racism and anti-Semitism.

"The voters who voted for Mr Melenchon are angry voters. They can be in agreement with us," said Steeve Briois, a vice president of Le Pen's National Front party. He said they express a choice "outside the system".

Choosing inside the system is no longer an option for French voters, who rejected the two mainstream parties that have alternated power for decades in favour of Le Pen and the untested Macron, who has never held elected office and who founded his own political movement just last year. Turnout was 78%.

Socialist candidate Benoit Hamon, whose party holds a majority in the legislature and whose President Francois Hollande is the most unpopular in modern French record-keeping, got just 6%. The conservative candidate fared marginally better, coming in third with just shy of 20% of the vote.

Both centre-right and centre-left fell in behind Macron, whose optimistic vision of a tolerant France and a united Europe with open borders is a stark contrast to Le Pen's darker, inward-looking "French-first" platform that calls for closed borders, tougher security, less immigration and dropping the shared euro currency to return to the French franc.

European stock markets surged on opening as investors welcomed the first-round results, with Macron favoured to win. German Chancellor Angela Merkel wished Macron "all the best for the next two weeks".

Le Pen's father, Jean-Marie, made it to the second round against Jacques Chirac in 2002 and was crushed. Many commentators expect the same fate for his daughter, but she has already drawn far more support than he ever did and she has transformed the party's once-pariah image.

Macron came first in Sunday's vote, with just over 23%; Le Pen had 21%; Melenchon and losing conservative candidate Francois Fillon each had 19%. Fillon, a former prime minister, bested the former Trotskyist by just 94,998 votes.