Now a global figure, a far-right populist who has threatened to bring down the European Union, Ms. Le Pen is at the threshold of power as France prepares for the final round of voting for president on Sunday. Her odds, judging by the polls, are long. But even if she does not succeed against the independent centrist Emmanuel Macron, Ms. Le Pen is likely to be a powerful fixture of French politics for years to come. She is a political veteran, a fierce debater and perhaps the ablest campaigner in the entire French political spectrum.

Yet she has made a risky bargain. She has cast off the xenophobic legacy of the National Front, and she has not. Her father never swayed from the hardest, most hate-filled of political lines. The daughter aspires to the presidency. She has made a very public campaign of “un-demonizing” — shedding the party’s bigoted heritage — even as skeptics still wonder if the effort is more tactical than genuine. Her unspoken gamble is that she can keep the National Front legacy even as she reassures millions of French that she has transcended it.

When Donald J. Trump won the American presidential election, Ms. Le Pen suddenly seemed part of a global populist vanguard. But if that populist surge appears to be peaking — for now — it is also true that Ms. Le Pen is no Mr. Trump.

Unlike him, she does not improvise her policies, which are the product of a decades-long honing of National Front ideology. That ideology is not sui generis, unlike Mr. Trump’s. Its roots are in classic French far-right thinking going back 100 years or more. Indeed, some reputable scholars think that France, not Italy, was the true birthplace of fascism at the turn of the 20th century.