I check Luxembourg message boards frequently and often see one mistake. There's always a question posted about a family from the Luxembourg region of Belgium. The family assumes the word Luxembourg must mean that they're from Luxembourg. They're half-right, but the assumption can make locating their family's records that much harder.
Luxembourg was originally much larger than it is today. Parts of the Grand Duchy - as I discovered this morning - are now contained in France, Belgium, and more. Take a look at the partitions of Luxembourg section on the Belgium Roots Project page to get a better idea of what country your family's home village belongs to now. Once you've made that step, you can begin accessing your family's records in the correct archive.