Forms: lME organyse, lME– organize, 15– organise.Etymology: < Middle French organiser to give an organic structure to (14th cent.), to play the organ (14th cent.), to provide with organs (1510–20; French organiser ) and its etymon post-classical Latin organizare to accompany on the organ (c1090 in a British source; already in Vetus Latina in sense ‘to play the organ’), to arrange (c1190 in a British source), to provide with bodily organs or physical structure (13th cent. in British sources) < classical Latin organum organ n.1 + -izāre -ize suffix.
Interesting that the history of "organize" so muddles up the bodily organs with the operation of the musical instrument; a look at the history of "organ" suggests that there were actually two separate ancient words (a feminine word for all things music, and a masculine word for the body stuff) that got mashed together in Middle English.
Just goes to show, you can't trust the Middle English.