Why is it nutmeg and not *megnut?
Is it something to do with Latin/French influences on the English grammar?
It is from Old French noiz mugue, probably influenced by Medieval Latin nux maga:
nutmeg (n.) :
"hard aromatic seed of the East Indies," c. 1300, from Old North French or Anglo-French noiz mugue, from Old French nois muguete, unexplained alteration of nois muscade "nut smelling like musk," from nois "nut" (from Latin nux) + Latin muscada, fem. of muscat "musky".
Probably influenced in English by Medieval Latin nux maga (compare unaltered Dutch muskaatnoot, German muscatnuß, Swedish muskotnöt).
(Etymonline)
Nutmeg (as reported by the OED):
NUT n.1 + a second element which is either Middle English muge musk (rare ...) or its etymon Anglo-Norman muge, mugue and Old French mugue musk (end of the 11th cent.; ultimately < post-classical Latin muscus MUSK n.), probably after Anglo-Norman nois mugette (also nois muscade, nois muscate) and Middle French noix muguette (14th cent.; 12th cent. in Old French as noiz mugate, noiz muguete, noiz muscade, noiz muscate, ...).
No compound in mugue musk, directly paralleling the English word, is attested in either Anglo-Norman or Old French, but compare post-classical Latin nux muga (1325), nux de muga (1314; both in British sources). Compare Catalan nou moscada ..., Old Occitan noz muscada (c1250), Italian noce moscata ..., Spanish nuez moscada ..., post-classical Latin nux muscata (see NUX MOSCHATA n.).
The Romance compound has been borrowed into several Germanic languages, compare Middle Dutch notemusscate (Dutch nootmuskaat, notemuskaat; also muskaatnoot denoting the fruit containing the nutmeg), Middle High German muscātnuz (German Muskatnuss), Swedish muskotnöt, Danish muskatnød. ...]
(www.wordorigins.org)