We do "Es ist ein Ros entsprungen" "Tomorrow Shall be my Dancing Day" Bring a Torch Jeanette Isabella" "Ding Dong Merrily on high(Bransle Officiel)" "Pat a Pan" "Seven Joys of Mary" "I saw three Ships/Sussex Carol (as a pair alternating tunes)" "Sir Richard de Coverly" and a few more.
Although the last is probably outside your timeframe, I think most of the others fit (without actually checking).
JohnB.