Unsophisticated (5)
(Other definitions for gauche that I've seen before include "Lacking grace" , "inelegant" , "'Lacking social polish, awkward (6)'" , "Graceless" , "Ill-at-ease, awkward in social situations" .)
(Other definitions for uncool that I've seen before include "Not with it (but warm?)" , "Not in fashion or with it" , "hot?" , "Not fashionable (colloq.)" , "Old-fashioned" .)
'unsophisticated' is the definition.
(synonyms)
This is all the clue.
(Other definitions for naive that I've seen before include "Simple and guileless" , "Without worldly wisdom" , "Simple in style or behaviour" , "Showing lack of maturity or judgement" , "Artless; simplistic" .)
(Other definitions for graceless that I've seen before include "Awkward" , "Indecorous" , "Lacking elegance" , "clumsy" .)