Middle English word reche comes from Proto-Indo-European *rewə-, Proto-Indo-European *rowgi-, and later Proto-Germanic *raukiz (Smoke, vapour.)

Detailed word origin of reche

Dictionary entry	Language	Definition
*rewə-	Proto-Indo-European (ine-pro)
*rowgi-	Proto-Indo-European (ine-pro)
*rewg-	Proto-Indo-European (ine-pro)
*raukiz	Proto-Germanic (gem-pro)	Smoke, vapour.
rīec	Scots (sco)
rīec	Old English (ang)
reche	Middle English (enm)

Words with the same origin as reche