Blank is a colour disguised as an absence. It comes from Old French blanc, meaning 'white', from Frankish *blank, 'bright' or 'shining'. In English it shed its colour and kept only the emptiness. In French, blanc still means white.
The transition makes physical sense. Before the printing press, a blank page was a white page — unmarked vellum or paper. To leave a space blanc was to leave it white. English kept the concept (empty, unmarked) and dropped the colour.
The Germanic root *blankaz meant 'bright' or 'gleaming' — not necessarily white. German blank still means 'shiny' or 'bare', as in a polished surface. The brightness-to-whiteness-to-emptiness chain shows how concrete sensory words drift toward abstraction.
Blanket belongs to the same family: originally a piece of white cloth, from Old French blankete ('little white thing'). Carte blanche — a 'white card' — sits at the exact intersection of the French and English meanings: an empty document awaiting instructions, white because it is blank, blank because it is white.