The tune is a bourrée, composed by the French hurdy-gurdy player Gilles Chabenat, who based it on a bit of Debussy. Properly called Les Poules Huppées, of which The Crested Hens is the English translation. Solas play it rather more slowly than its composer intended; it's a dance tune really, not a slow air. It used to be played quite a lot in English sessions (at original speed and usually under its French title); I believe Solas picked it up in a London pub. I didn't realise there were now people out there who think it's an Irish tune.