It marks just the latest setback for the mainstream left across Europe — a retreat that has been largely missed by media reports as they focus on far-right leaders, whether they win or lose.
Hamon, part of the same party as incumbent President Francois Hollande, appears set to finish fifth in the vote based on early indications from pollsters. Centrist Emmanuel Macron and far-right candidate Marine Le Pen looked set to finish first and second, respectively, according to exit polls, setting up a runoff next month.
Old guard liberals are fading across the continent, as politics become a battle between nationalist populists and more global centrists.
The British Labour Party — Britain's second-largest — lost 26 seats in the House of Commons in 2015 elections, while the center-left Liberal Democrats dropped 49 seats. The Conservative Party — already Britain's largest, and containing both global and populist elements — gained 24 seats.
In the Netherlands this year, centrist Prime Minister Mark Rutte kept his job ahead of far-right Geert Wilders and the Party for Freedom. Media coverage focused on Wilders' defeat, and it largely ignored what happened to Dutch liberals: The country's mainstream left Labour Party dropped 29 seats in the parliamentary elections.
In a March, Chancellor Angela Merkel's center-right Christian Democrats won a regional election in Germany's Saarland state, while the center-left Social Democrats saw their vote share dip slightly from the area's last election in 2012. The result by the Social Democrats was by no means catastrophic, but some saw it as a possible bellwether for the national election later this year.
—CNBC's Ted Kemp contributed to this report.