The song he sings is effectively named "Morning's Here" because that's its first line. It is actually based entirely on a Chuck Mangione track called "Feels So Good" on which his virtuoso french-horn performance kicks a bit of Jazz guitar up and down groove street (Chuck of course being mentioned numerous times in Friends, for instance in the episode with the beach house where phoebe tries to find her father and finds her mother instead) but the words are made up. So infectious is it, that you just can't stop singing it, just as I never grow tired of hearing it. The lyrics are these:
"Morning's Here
The Morning is Here
Sunshine is Here
The Sky is Clear
The Morning's here
Get into Gear
Breakfast is near
The Dark of Night Has Disappeared"