Don is not quite right. Although the popular image of the troubadour is of a wandering entertainer, such people were actually known as Joglars in Langue D'oc or Jongleurs in Langue D'oeil. In their own time, the people known as "troubadours" were primarily noblemen, ranging in status from Dukes to knights. Some of the later troubadours were artisan-class (eg. Bernart de Ventadorn, who seems to have been the son of a baker). But mostly, it was an aristocratic occupation.

Minstrels in England were more analogous to the jongleurs than to the troubadours.

I agree that there's certainly no harm in Sting trying his hand at this, and that the results are pleasant enough. He's an easy target, though!