Fur
Middle English (as a verb): from Old French forrer ‘to line, sheathe’, from forre ‘sheath’, of Germanic origin.
wiktionary
From Middle English furre, forre, from Anglo-Norman forre, fuerre(“a case; sheath”), from Frankish *fōdar, from Proto-West Germanic *fōdr, from Proto-Germanic *fōdrą(“sheath”) (compare Old English fōdor(“sheaf”), Dutch voering(“lining”), German Futter(“lining”), Gothic 𐍆𐍉𐌳𐍂( fōdr, “sheath”)), from Proto-Indo-European *peh₂-, *poh₂-(“to protect”) (compare Lithuanian piemuō(“protection”), Ancient Greek πῶυ(pôu, “flock”), πῶμα(pôma, “lid”), ποιμήν(poimḗn, “shepherd”), Old Armenian հաւրան(hawran, “herd, flock”), Northern Kurdish pawan(“to watch over”), Sanskrit पाति(pāti, “he watches, protects”).
The verb is from Middle English furren, from Anglo-Norman furrer, forrer, fourrer(“to line, stuff, fill”), from the noun.
fur
etymonline
fur (n.)
late 14c. "trimming or lining of a garment" (implied c. 1300 in surname Furhode "fur hood"), probably from Old French forrer, fourrer "cover with fur, line (clothing)," in general "to cover, fill with," from fuerre "sheath, scabbard" (via notion of "covering"), from Frankish *fodr or another Germanic source, from Proto-Germanic *fodram "sheath" (source also of Old Frisian foder "coat lining," Old High German fotar "a lining," German Futter, Gothic fodr "sword sheath"), from PIE root *pa- "to feed, protect."
First applied c. 1400 to the hairy pelt of an animal, whether still on the animal or not. The Old French noun might have had the sense "hide, fur, pelt" (and thus might serve as the immediate source of the English noun), but this is not attested. Absent this, the sense transfer from the lining to the material that goes to make it probably happened in English. As an adjective from 1590s.
I'le make the fur Flie 'bout the eares of the old Cur. [Butler, "Hudibras," 1663]
fur (v.)
c. 1300 (implied in furred), from fur (n.) or Old French fourrer "to line." Related: Furring.