Actually, the deacon (or priest) sings "O Happy Fault," not at Christmas, but at the Easter Vigil, in a long poem/preface called the Exsultet, from its first word in Latin.  (Until the liturgical reforms of Pius XII took effect in 1955, the Exultet-- as it was spelled in those days -- included a lenghthy intercessort prayer for the Holy Roman Emperor!) 

Had you read or remembered beyond "O Happy Fault," you would have discovered the following text:  "Huius ígitur sanctificátio noctis fugat scélera, culpas lavat, et reddit innocéntiam lapsis et mæstis lætítiam.  Fugat ódia, concórdiam parat et curvat impéria." (The sanctifying power of this night dispels wickedness, washes faults away, restores innocence to the fallen, and joy to mourners, drives out hatred, fosters concord, and brings down the mighty.)  

The BIG difference here is the focus on Jesus as Savior -- as Father Tom Reese does -- rather than directly on the seven deadly sins of man [sic].