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mid-13c., "skin or fur of the marten," from Old French martrine "marten fur," noun use of fem. adjective martrin "of or pertaining to the marten," from martre "marten," from Frankish *martar or some other Germanic source, from Proto-Germanic *marthuz (cf. Old Saxon marthrin "of or pertaining to the marten," Old Frisian merth, Middle Dutch maerter, Dutch marter, Old High German mardar, German Marder, Old English mearþ, Old Norse mörðr "marten"), probably from PIE *martu- "bride," perhaps on some fancied resemblance, or else a Germanic euphemism for the real name of the animal, which might have been taboo.
In Middle English the animal itself typically was called marter, directly from Old French martre, but marten took over this sense in English c.1400.