Olivier Krug has a job that many people would envy. The 43-year-old represents the sixth generation of the Krug Champagne dynasty and travels the world drinking and promoting the brand, whose cheapest bottle of Grande Cuvée sells for at least €100 ($135).

But Mr. Krug is not master of all he savors. He has to balance his affection for the Champagne house founded by his family in 1843 with the demands of a multinational corporate owner.