White beret for two reasons: firstly, the unit originally chosen for parachute training was descended from arctic riflemen/militia/specialist regiment (basically, who wore a grey-white uniform). When allocating beret colours they received white ones because of the tradition. Another of the units which formed initial airborne elements had blue ones, but demanded to swap to white ones for reasons of ego and bullshit. They were assented to, and ultimately that started the spread of the white beret.
This is the origin of the slang for a paratrooper in Kouralia who arrogantly sees their paratrooper status as making them innately 'better' than someone from the regular infantry (usually in situations where being able to jump out of a plane makes little difference to capability) as a 'special little snowflake' (best said in an over the top mocking tone, as if addressing a five year old "Aren't you a special little snowflake?").