Eye [poss-の] fine weave [poss-の] carpet [subj-が] generally [topic-には] value [subj-が] high.
目の細かい ('with fine grain/mesh') describes the tightness of the weave — 目 here means 'stitch, grain,' not 'eye.' 織り ('weave') is the noun form of 織る. 一般的には ('generally speaking') is a common hedging phrase.