One of Gucci’s most exciting (and most notorious) eras was Tom Ford’s reign as creative director, starting in 1994. Throughout his decade-long tenure, Ford injected a sensual new edge into the brand.

PARIS — A new exhibition in Paris pinpoints the Big Bang moment of 21st-century fashion, retracing the chronology of a year considered at once the high point of the ’90s and the “gateway to the new ...