You have heard one of his compositions, and likely can sing along to it. Here's the song:
Adam was what you might call a "natural". As a child, he didn't like his structured music lessons, preferring to improvise. He was a prolific composer of operas and ballets, and a professor at the Paris Conservatoire. His music is very listenable, and he really deserves to be know for more than a single Christmas carol.
Today's classical composition is the overture to the comedic opera Si j'étais Roi (If I were King):