Liberal centrist Emmanuel Macron - winner of the first round - and nationalist Marine Le Pen are already revolutionising French politics.
They have delivered a big blow to the long-dominant Socialists and conservative Republicans.
Mr Macron leads a new movement called En Marche (On the Move), while Ms Le Pen is backed by the National Front (FN). They disagree on many issues, especially Europe and immigration.
The decisive second round is on 7 May - and polls suggest Mr Macron is ahead. So what are the main differences between the Macron and Le Pen visions?
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Last updated  April 25, 2017
The polling average line  looks at the five most recent national polls and takes the median value, ie, the value between the two figures that are higher and two figures that are lower.

One woman was injured on Wednesday's incident, which led to dozens of nudist sunbathers fleeing Carataggio beach near Porto-Vecchio.
Witnesses said the man had threatened the group if they did not get dressed.
When they refused, he allegedly pulled out a rifle and started firing.
The injured woman, reportedly in her thirties, was hit in the thigh as she ran away.
The suspect - whose identity has not been revealed - owns a beachside cafe, police said on Friday. One man had been questioned in connection with the shooting but had since been released.
Despite being famous among nudists, the beach is not an official naturist site and locals have complained about their presence there.

Robinson, 21, who previously had two loan spells at the Lilywhites, turned down a new deal with Villa and joins for an undisclosed compensation fee.
Newcastle-born former Rotherham man Pringle, 26, signs for an undisclosed fee after one year with the Cottagers.
Pringle made nine league starts during a short loan spell at Ipswich in 2016.
Robinson told the club's website: "It was obviously a big decision for me leaving Aston Villa, I've been there since I was eight-years-old.
"But, if there was ever a club for me to settle down with and sign permanently with, it would be Preston North End."
Find all the latest football transfers on our dedicated page.

Sheikh Obeikan, who was an adviser to the royal cabinet, opposed moves to relax gender segregation.
The dismissal comes shortly after Sheikh Obeikan attacked plans by "influential people to corrupt Muslim society by trying to change the natural status of women".
Saudi officials did not give a reason for Sheikh Obeikan's departure.
His recent comments were taken to be an attack on tentative steps towards relaxing some stricter interpretations of Saudi law.
King Abdullah has promised women the right to vote in future elections, has opened the country's first co-educational university and introduced measures against domestic violence.
The head of Saudi Arabia's religious police, the "mutawa", was also replaced in January, with the new head widely seen as more moderate than his predecessor.
Sheikh Obeikan achieved a degree of notoriety several years ago with a decree suggesting that unrelated Saudi men and women could mix so long as the man drank the woman's breast milk, thus creating a maternal bond between them.
National renewal is what both the rival French presidential candidates are promising, but they offer very different paths to get there.
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A shootout on a beach popular among naturists on the French island of Corsica was caused by a local businessman who disagreed with their presence there, police say.
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Championship side Preston North End have signed Aston Villa forward Callum Robinson and Fulham midfielder Ben Pringle, both on three-year contracts.
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Saudi King Abdullah has sacked one of his most hardline advisers, Sheikh Abdelmohsen al-Obeikan.