Last Sunday, in the hours after the first round of the French presidential election, the top two finishers both held rallies. But it was the No3 candidate who gave the victory speech.

With tricolors waving everywhere, Marine Le Pen strode out like a prize fighter, having notched the best result ever for the Front National, the party her father founded 40 years ago. Le Pen made the usual sounds of the hard right, attacking "the system" and "the elites" and "lies and false opinion polls". But she got her greatest applause when she praised her supporters with this line:

"All of us, together, have blown apart the monopoly of the two parties of the banks, of finance, of multinationals, of giving up, of abandonment … But this is only the beginning."

The next day, triumphant on the French national news, she dissed François Hollande and Nicolas Sarkozy as "not candidates for president", but pawns in the hands of the Germans and the European Central Bank. Since then, she has kept it up, hitting out at big business and especially big banks – and reminding us that the European hard right is not so much like ours.

Le Pen's quasi-victory came the day after the government of the Netherlands collapsed; Geert Wilders, the Islamophobic demagogue who leads the third-largest party, pulled the plug on the Rutte government after just 18 months. You might remember Wilders, with his tuft of blond hair, for his senseless Qur'an-trashing documentary (screened in the US congress, let's recall, at the request of Senator Jon Kyl). But Wilders didn't precipitate early elections over social issues – it was budget austerity he disapproved of. For all his hatred of Islam and immigrants, Wilders is going to the polls as an opponent of permanent euro-bailouts and a defender of the welfare state.

We reflexively describe Le Pen and Wilders and their parties as "the extreme right," but as the economic crisis continues to upturn politics on the continent, that description more than ever fails to capture what's going on. For a start, they have left behind the fascist overtones and Holocaust denial of the old European hard right (though that endures, certainly, everywhere from Britain's BNP to Hungary's terrifying Jobbik). More than that, these new hard right leaders, whom we should probably call "right populists", are defenders of a mythical status quo – and while that means white and Christian, it also, less evidently, means a time before globalization and the sovereign debt crisis threatened the certainties of voters, particularly older ones.

In the US, we still think of the extreme right as anti-government, but these right-populists often thrive in countries with strong welfare states, from Finland to Austria. Indeed, the most successful right populist of them all might be Pia Kjærsgaard of Denmark, which has the highest welfare spending of any country in the OECD. Back in the 1990s, her Danish People's party was one of the first to link up xenophobic social policy and anti-Muslim rhetoric with generous public spending promises; and until the last election, she was so powerful that she was propping up the government in exchange for both immigration controls and cash for seniors.

If that all sounds a bit unnatural to American ears, that's only because the right in the US is so thoroughly entrenched within the logic of corporatism that we cannot even conceive of another kind of right wing. Every now and then, a seeming right populist politician bobs to the upper echelons of the Republican party, usually an evangelical Christian like Mike Huckabee in 2008, or Michele Bachmann this time around. But their posturing to speak for Main Street, and the church sitting thereupon, never converts into dollars and cents. They are "Pinos", populists in name only: sooner or later, they always end up endorsing radical anti-tax proposals that favor the rich and sometimes actively penalize the poor (as in the 9-9-9 plan of the thankfully sidelined Herman Cain); elimination of public services, welfare protections like social security, and even healthcare; and increased spending on nothing except bombs over the "Islamofascist" enemy of the day.

Until the crisis, you could blame this on a bait-and-switch by the right-wing establishment: fool the working class with social wedge issues such as gay marriage or gun control, then cut yourself a massive tax break and leave their public services to fester. But after the crash of 2008, and with the Tea Party phenomenon that rose from its ashes, we can no longer say that working-class religious or nativist voters are being hoodwinked. Reaganite hatred of government runs deep in America, and as Thomas Frank detailed in his recent book, Pity the Billionaire, the Tea Party and other elements of the new right know with unqualified certainty that business is their champion and government their foe. In the wake of the biggest failure of laissez-faire capitalism most of us have ever witnessed, fans of Glenn Beck (remember him?) followed his lead and donated millions of dollars to the US chamber of commerce, not exactly a defender of the little guy. They make no distinction between the corner store and Chrysler; "let the failures fail," they scream, whatever the cost.

The American right's mythical constitutionalism and where's-the-birth-certificate Islamophobia have the same roots as Europe's right populism: globalization, relative economic decline, and a sense that the political establishment isn't listening to them. But the ideology it has led to here in the US would be unrecognizable, not to say scary, to a backer of Le Pen, Wilders or Kjærsgaard. For while the rhetoric of the American right appeals to enduring, conservative principles, its actual ideology is shockingly radical. Rick Perry's notorious slip-up at one of the thousand or so Republican debates last year, at which he proclaimed he would junk three entire cabinet-level departments but couldn't remember which ones, surely gave the game away: destruction of the public sector is the name of the game, and the beneficiaries of that destruction will not be voters on the right, but the corporations and one-percenters with whom they have knowingly, absurdly aligned themselves.

Our friends in France and the Netherlands face a struggle to combat intolerance and reintroduce swaths of voters back into the mainstream, but here in America, our job might be even tougher. Our fight against intolerance is hard enough. But we also have to fight the chokehold of big business and financial markets on the American imagination – and find a way of reminding ourselves that there is still such a thing as the public good.