This spring America belongs to a Frenchman. Not some world-weary actor, voluble television chef or suave and elegant wine-maker, representatives of trades that on this side of the Atlantic are seen as France's prime contributions to civilisation. No, the Anglo-Saxon superpower is in thrall to a tousled, left-leaning, Parisian economist, aged 42, named Thomas Piketty, and his doorstop of a tome on income distribution in the western world.

Capital In The Twenty-First Century, all 685 pages of it, is the No 1 best-seller on Amazon – apparently the first time that anything published by the venerable Harvard University Press has attained such dizzying celebrity. No self-regarding dinner party in Washington or New York is worth its salt without a discussion of it. Last Friday, came the ultimate accolade of a multiple coronation on the op-ed page of The New York Times.

On the left-hand side was a column entitled "The Piketty Phenomenon", by David Brooks, the paper's sensible-conservative-in-residence. Running down the right of the page was an Olympian blast from the Nobel prize-winning liberal economist Paul Krugman with the headline "The Piketty Panic", arguing that conservative economic doctrines that were ruining America had finally been put to the scientific sword.

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One way and another, there is simply no escape from the man, and in the process every national stereotype has been turned on its head. Where are all those "cheese-eating surrender monkeys"? Instead, Piketty is being hailed, by the left at least, as the Frenchman most expert on – and sympathetic to – the United States since Lafayette and De Tocqueville some two centuries ago. The potential impact of his work is being compared by admirers to Karl Marx's Das Kapital or John Maynard Keynes's General Theory.

The central thesis of Capital in the 21st Century is that, left to its own devices, the capitalist system will increase the gap between rich and poor, as it always has done. Since the dawn of the industrial era, in countries such as Britain, France and the US, the return on investment and capital has been greater than the return on labour. According to Piketty, the mid-20th century, when these trends reversed, was an aberration, as two world wars and the Great Depression destroyed many great fortunes, and redistributive social democratic policies carried on the process in the immediate decades after 1945.

Now, however, he says, the pattern is reverting to type. A disproportionate share of wealth is going to capital; the more "perfect" the market, the more pronounced this trend will be. The West, in short, is in a new Gilded Age, where an ever greater share of the national pie is held by the same families, and passed down from generation to generation. Left unchecked, this unfairness will bring social resentments and tensions that will undermine democracy. In Piketty's view, only government action – that is some form of tax on wealth – can reverse the trend.

But why the fuss now? Piketty's historical research may be unprecedently comprehensive, but the condition he diagnoses has been known about for ages. Since the 1980s, middle-class incomes here have stagnated, while the seriously rich have grown rapidly richer. Widely reported studies have shown that disparities of wealth are greater than at any moment since the 1929 crash – even that the social mobility and opportunity for which the US has always been famed, are now less than in sclerotic "Old Europe".

So what else is new? Fads and hype are as American as apple pie: is not the Piketty phenomenon just another example? Maybe, and in a few months we'll have forgotten his name. But maybe not. Maybe Piketty is articulating an idea, albeit familiar, whose time at last has come. America's pride has long been its middle class. The core of the "American Dream" was the promise that anyone prepared to work could climb from nowhere to the sunlit plateau of a steady job, a couple of cars in the garage and a decent pension. Nowhere else was this so possible for so many and for so long as in meritocratic America.

Now, this concept lives only in the vapid slogans mouthed by politicians at election time. Real people know from the evidence of their eyes that old certainties have long vanished, that many jobs lost will never come back, and that money calls the shots. If proof were needed, last week provided it, with a study in The Times showing that in Canada and many advanced countries, the middle classes are doing better than in the US, where unions were weak, taxes lower, and a disproportionate share of new wealth went to those who already had plenty.

And Piketty is not the only one making the point in print. Also in the top five Amazon best-sellers are A Fighting Chance by Elizabeth Warren, Democratic senator from Massachusetts and heroine of the left, who made her name as a consumer champion and scourge of Wall Street and corporate America; and Flash Boys by Michael Lewis, exposing the shady universe of high-frequency traders. At bottom, all three books are about the same thing – how the system is rigged against the little guy, in favour of the rich.

Something, surely, is stirring and if US history is any guide, the protest will show up in politics, sooner rather than later. Ms Warren's most fervent supporters urge her to run for the Democratic presidential nomination, even against Hillary Clinton, and even though she says no.

Republicans, the traditional party of the rich, have long finessed the problem, saying the wealthy were "job creators" who deserved their good fortune, and that anyone who differed was jealous, petty-minded and, well, un-American. But for how much longer, if the supposedly meritorious rich are merely a self-perpetuating rentier class whose ranks are increasingly hard to join? After the Piketty Phenomenon and the Piketty Panic, could there be a Piketty Election in 2016?