speak smb.'s language

(speak (или talk) smb.'s (или the same) language)

найти общий язык с кем-л.; см. тж. speak a different language

Bobby... had presumed that since he and I "spoke the same language", I should naturally dislike the Director as much as he did. (A. Wilson, ‘The Old Men at the Zoo’, ch. 1) — Бобби... считал, раз мы нашли с ним общий язык, я, естественно, должен испытывать к директору такую же неприязнь, какую испытывал он.