Blue Bayou is written in the key of F Major.
According to the Theorytab database, it is the 6th most popular key among Major keys and the 6th most popular among all keys. Major keys, along with minor keys, are a common choice for popular songs. The three most important chords, built off the 1st, 4th and 5th scale degrees are all major chords (F Major, B♭ Major, and C Major).
See the F Major Cheat Sheet for popular chords, chord progressions, downloadable midi files and more!