Emmanuel Macron, a centrist and political quasi-neophyte, has been elected president of France against populist leader Marine Le Pen. While these candidates' positions are diametrically opposed, they agree on one thing: They are sui generis political figures whose performance hails a fundamental realignment of French politics. And most commentators agree with them: We have all noticed now that the pressures of globalization and technology are splitting advanced Western economies into underclass and overclass, and that this rift scrambles the cards politically. Both Brexit and Donald Trump were "right-wing" phenomena propelled to victory thanks to the votes of working-class natives whose traditional allegiance lay with the left.

Except that closer scrutiny of the data shows that, when it comes to France at least, what is happening is not so much a transcending of the old left-right divide as a realignment within each side of this great divide.

Let us first give the "great realignment" thesis its due. Macron drew from both left- and right-affiliated voters in both rounds. Meanwhile, Le Pen does draw a lot of her electoral strength from working-class voters who, in a previous era, might have voted for the Communist Party.

That's all true, and yet the argument against the great realignment is stronger. Macron drew from both left and right, but in the first round many of his right-wing backers voted for him more out of disdain for the scandal-plagued conservative François Fillon than out of belief in some new centrism. In the second round, Macron benefited from the "Front républicain," or the rejection of Marine Le Pen's National Front by the overwhelming majority of the French political class. According to second round exit polls, 59 percent of Macron voters said they voted for him to reject the other candidate.

On Marine Le Pen's side, the data is even more clear. Le Pen's great bet was to build a coalition of the far-left and the far-right and unite the working class under her. This has been a failure. Despite her repeated appeals, only 7 percent of the people who voted in the first round for Jean-Luc Mélenchon, the "anti-establishment candidate" on the left, voted for her in the run-off. By contrast, between the first round and the second round, she saw the most gain among conservative voters: She won 20 percent of those who voted for François Fillon, and 30 percent of those who voted for Nicolas Dupont-Aignan, the other conservative candidates.

In other words, politically, Marine Le Pen remains a far-right candidate; she does have a working-class constituency, but her natural electorate remains voters who traditionally vote for conservative parties. And the French right, like the American right, has had a working-class component in its coalition for a very long time. I attended Marine Le Pen's last rally in the presidential election and spoke to many of her supporters; while the overwhelming majority were working class, most of them were former Sarkozy voters, not left-wing voters. Crime and immigration were their top issues, alongside the economy. And on the economy, they blamed France's economic woes equally on globalization and on regulations and taxes holding back small business; they had no love for big business, but this was out of a feeling that the system is rigged, not out of any ideological left-wing hostility to business and entrepreneurship.

Meanwhile, Macron's coalition remains tilted to the left. While he definitely grabbed voters from the right and the center, the left turned out for him more. What's more, while the Socialist Party is keen to work with him, Les Républicains, the main conservative opposition party, has stated that if it wins the legislative elections, it intends to rule the country without him and that any Republican who joins Macron would be ejected from the party.

In both cases, then, each candidate shifted the dynamic within their own side, but if you look beyond the spin, the left-right divide actually seems more alive than ever. In American terms, then, the parallel to Macron would be not so much a Michael Bloomberg-style centrist independent winning the presidency, but rather a Bill Clinton, who manages to drag his side to the center, but without fundamentally realigning the country's politics.

Keeping with the American parallel, the closest analogue to Marine Le Pen would be a Barry Goldwater figure, too radical for the population at large, but whose performance means her ideas and voters can no longer be ignored by her side, especially within the context of an establishment consensus that has lost credibility. This would suggest that French politics still awaits its Nixon or Reagan, a conservative figure who can find the right mix of populism and respectability to draw together the country's "silent majority" into a winning coalition.