In the European Union, "Champagne" is a Protected Designation of Origin, and so cannot be used within the EU on wines (especially sparkling wines) which do not originate from the Champagne wine-producing region of France. Several other countries have also granted some protection to "Champagne" in connection with wines. I believe this is mainly what the "champagne" domain name fights have been over.
As far as I know, this protection does not extend to books, music albums, or other products which would not infringe upon the Protected Designation of Origin.
Of course, this only answers a part of the question, since the name "Champagne" in connection with products other than wine has been registered (such as Champagne Apples). So, it would probably be wise to research your individual use of the mark in each of the jurisdictions in which you plan to use it in order to look out for possible infringements.