She paled at the news.

Literal

She [topic-は] that news [object-を] hearing [then-て] blue became.

青くなる literally 'turn blue,' here meaning 'turn pale' — Japanese routinely uses 青 ('blue') for the bloodless complexion of fear or shock, where English reaches for 'pale' or 'white.' Without the intensifier 真っ, the effect is somewhat softer than 真っ青になる. 青く is the adverbial form of the i-adjective 青い ('blue'), and ~くなる is the standard pattern for change of state. Note Japanese has a long history of overlapping 青 and 緑 ('green') — traffic lights are still officially called 青信号 even though they appear green, a holdover from an older color taxonomy.