Isn't it pretty standard to pull or trim and band a mane for those classes? I don't know if a running french braid would be allowed. If there is no requirement on how to style it, I would either do the running braid or just leave it loose.
I know in showmanship they like short pulled manes with banding or sometimes just nice neat pulled manes. Are you going to a school show? if you are then your mane shouldn't be a big deal. If it's a breed show of some kind you can always check your rule book for grooming requirments. Another thing you can do is call the show manager and see if he/she has any suggestions for how you can style her mane. Hope I helpedI have a big show coming up and I have a mare that has a long mane I am going to show her in showmanship and weastern pleasure. Does anyone know how I should style her mane without pulling or cutting it??? I love her long mane. Please reply soon show is coming up!!