Well, every larger city has a school I think. Maybe they even went to the town were the "girl-friend" lived, and it was her school. I think this isn't important for what the film wants to tell, and it also makes the scene more fun. When "Gianni" goes "to look for her" and he is watching the biathlon team, I find the contrast between their speed and Paolo's handicap startling. We are also guessing all of the time if one of the girls might be her. 
The "girl-friend" is an emblem for Paolo's desires and what will probably become a big problem when he gets older. I like the scene where Gianni comments on Paolo being a teenager and not a kid earlier in the film. Thus it's not important who the girl is, imo. 

What i also appreciate is the fact that the film's flawed protagonist has the same name as the director. I always appreciate these little touches (as well as the dedication at the beginning of the movie).