So I dug up my old "Quidditch Through the Ages" and this is what it says about broom sports.
There is an annual broom race in Sweden. It is a three hundred mile race that passes through a dragon reservation.
The Germans play Stitchstock. But it died out in the fourteenth century. (Modern revival perhaps?)
Aingingein was played in Ireland. It is a type of obstacle course on broomstick.
Although it is banned, Scotland once played the deadly Creaothceann.
Shuntbumps is a form of jousting on broomsticks popular in Devon, England. It is still a children's game.
Swivenhodge was also played in Herefordshire, England. Players use the end of their brooms to swish an inflated goats bladder across a hedge.
I hope this helps!