Obviously Greg is utterly right. The question, however, can be specified in
1. the oldest song preserved in writing
2. the oldest song still sung
and so on.
For 2: look for church songs, using such antique browsers as hymnals &c. Gregorian hymns are still in use today, and in my Lutheran songbook there are some tunes slightly changed to the German translations of their old Latin texts, going back to Ambrosius and the like.
The farther some old songs go back the more difficult it is, naturally, to be sure which is the oldest of them.
For questions of this kind the European churches can't be omitted, true to their conservative strains.

Wilfried