Turquoise is also the adjective referring to the color of the gem.
Surely the French for turkish is turc? or turque, if feminine? I've never encountered Turquoise meaning turkish, only the gem or the colour associated with the gem....Quizmonster, can you clarify? Sorry about that...just curious!
In Old French, 'Turkish' was 'turqueise' and later 'turquaise' before becoming 'turquoise'. Originally, this always referred to the gem...ie as 'pierre turquoise' (Turkish stone)...since it was found in Persia and Turkestan.
As a colour, there is no record of it in English before the middle of the 19th century.