The French PR will be reunited with Hedi Slimane, with whom she previously worked at Dior Homme and Saint Laurent.
The executive will lead Louis Pion, Galeries Lafayette-Royal Quartz Paris and Augis 1830.
The retail veteran has worked at Fenwick of Bond Street and Selfridges.
The denim company said the executive will remove himself from the firm’s day-to-day activities.
The Gap president is leaving after almost 15 years with the brand.
Brunschwig, who was previously Dior Homme chairman and ceo, will report to Antonio Belloni, LVMH Group managing director, succeeding Pietro Beccari, who is now chairman and ceo of Christian Dior Couture.
The luxury giant’s four-month program includes a contest for the luxury experience of the future.
Adam Brotman has a history of digital retail initiatives.