You are
England
I have northen football that can unite
Manchester is in northern England, and has a football club called United
A flying city that will always fight
Not sure about this one. London is one of Europe's premier air traffic hubs, and Londoners are notorious for football-related violence (although I suppose that applies to the English in general).
Festive in the south
Southern England has popular vacation spots (Brighton, Eastbourne, Torbay)
A big man with a mouth
Jason Bourne is a big man, Bournemouth is a city in England
And mistaken as the greater might
Sometimes mistakenly used as a synonym for the UK as a whole