PARIS—For more than a year, French presidential candidate Marine Le Pen, representing the once-ostracized National Front, met with influential bankers, corporate executives and government officials to get advice on the radical changes vowed by her campaign. Now the group is helping plan what she hopes will be her first 100 days in office.

Ms. Le Pen has dubbed these members of France’s elite “Les Horaces,” a reference to the poet who penned verses for the first Roman emperor. It’s a measure of her rise that she has lured...