1650s (adj.); 1660s (n.), from Gaul + -ish. Earlier was Gaulic (1610s).
Entries linking to gaulish
Gaul n.
1560s, "an inhabitant of ancient Gaul," from French Gaule, from Latin Gallia, from Gallus "a Gaul." Also used somewhat facetiously for "a Frenchman." Gauloise, the popular brand of French cigarettes, dates to 1910.
-ish
adjectival word-forming element, Old English -isc "of the nativity or country of," in later use "of the nature or character of," from Proto-Germanic suffix *-iska- (cognates: Old Saxon -isk, Old Frisian -sk, Old Norse -iskr, Swedish and Danish -sk, Dutch -sch, Old High German -isc, German -isch, Gothic -isks), cognate with Greek diminutive suffix -iskos. In its oldest forms with altered stem vowel (French, Welsh). The Germanic suffix was borrowed into Italian and Spanish (-esco) and French (-esque). Colloquially attached to hours to denote approximation, 1916.
The -ish in verbs (abolish, establish, finish, punish, etc.) is a mere terminal relic from the Old French present participle.