The main difference between a Bourbon Stardust Soiree and a French 75 lies in the base spirit and the addition of elderflower liqueur. While a French 75 uses gin as its base spirit, a Bourbon Stardust Soiree uses bourbon, providing a richer and warmer flavor. Additionally, the Bourbon Stardust Soiree includes elderflower liqueur, which adds a floral touch, while the French 75 does not have this ingredient.