The lady smiled at me with friendly brown eyes.

Literal

Lady [topic-は] friendly brown eyes [with-で] me [to-に] smiled [polite-ました].

人懐っこい means 'friendly/approachable' — literally 'person-familiar.' 茶色の目 = 'brown eyes.' 微笑む (ほほえむ) means 'to smile gently.'