Following Meyer-Lübke (REW 1700), the French linguist Xavier Delamarre1 proposes Gaulish *karmon- as the source of Rhaeto-Romance (Surselvan) karmún 'weasel', although personally I think the source language would be Italoid.
This is a regional IE word *k´ormon- 'weasel, ermine' found in OHG harmo, Lithuanian šarmuõ 'wildcat, ermine', šermuõ 'weasel, ermine' as well as Basque armindderi (Aezk), armonddegi (HN), ergoniri (HN), ergoneri (HN), ergenore (HN), erbindori (*L), erminori (HN), erbiñore (G), erbiñude (G), erbiñure (G, L) 'weasel' (a compound whose second member is unknown2), with loss of the initial stop due to Martinet’s Law.
Probably related is Mongolian *keremü 'squirrel', borrowed into Tungus keremun (MT 123)3. There’re also Turkic *Küŕen, Mongolian *kürene 'ferret, weasel' (EDAL 1105) and Tungusic *gurma- / *gurna- 'hare; squirrel; ermine' (EDAL 572), wrongly linked to different words in other Altaic languages4.
1 X. Delamarre (2008): Dictionnaire de la langue gauloise, p. 105.
2 The forms erbi-unide (Bazt), erbionide (HN) are the product of a folk etymology from erbi 'hare' and unide 'wetnurse'.
3 G. Doerfler (1985): Mongolo-Tungusica.
4 In fact, the latter is absurdly paired to Turkic and Korean words meaning 'antelope; deer'.