I am just thinking about when the schools both entered the Great Hall for the first time at Hogwarts. Beauxbatons would obviously be represented by the color blue and Durmstrang could easily be associated with red because of the fire when they were first introduced. Just a thought... could be a story line where we, as Hogwarts students, are asked to choose a side to help. Obvioiusly if they put Hogwarts in as a school everyone would pick that one...
Just trying to figure out how the red and blue might be able to work on the track!