Sure, her father, Bernard Arnault, is France’s richest man and the head of LVMH, the world’s largest luxury goods company—but Arnault fille has business smarts and savvy in her own right.

Bernard Arnault, the 76-year-old billionaire founder of LVMH, signaled he could helm the luxury group for the best part of another decade.LVMH said in a filing that it will seek to raise the age limit ...