If you're considering a different cooking method, see this page too.
We call it "gîte sausage", because we always make it on vacation in a gîte in the Haut-Doubs, and there's no good vacation in the Haut-Doubs without gîte sausage.
And to drink?
Without a moment's hesitation, a white wine from the Jura, if possible a Savagnin grape variety. Its extraordinarily dry, fruity taste and nutty aromas go perfectly with Morteau. I suggest you take a look at my good addresses page to find out who my favorite supplier is.