The vast exposition hall in the dilapidated southern French town of Perpignan was standing room only on a recent Saturday, and the crowd was chanting, as if for a sports star: "Marine! Marine! Marine!"

When Marine Le Pen, the charismatic and complicated leader of the National Front, the largest far-right party in France, strode onto the stage, they shouted, cheered and then, with little prompting, soberly began to sing "La Marseillaise," the French national anthem.

Long prominent as the daughter of the National Front's founder, Jean-Marie Le Pen, who is widely considered anti-Semitic and xenophobic, Ms. Le Pen now appears to be transforming the party from a fringe player in French politics into a far more central one. She has moderated her party's image and positioned it to seize on widespread economic insecurity, deep anti-immigrant and anti-Muslim sentiment, and disgust with the political establishment.

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