Reich's smooth second run gave her a combined time of 1 minute, 51.80 seconds over Sarka Zahrobska of the Czech Republic (1:52.57) and Finland's Tanja Poutianen (1:52.89).
Denise Carboni of Italy finished fourth, one one-hundredth of a second behind Poutianen.
Lindsey Vonn of the United States was in second after the first run despite racing with a broken thumb but went down in the second as did Marion Bertrand of France, who skied aggressively with a large and loud French crowd at Val d'Isere urging her on.
The event was the final women's race in the FIS Alpine championships. Poutianen earned two bronze medals in the event. Vonn won two golds and Lara Gut of Switzerland took the silver twice.