In a peaceful and free atmosphere, they talked for a long time.
Literal
Peaceful and free atmosphere's inside [in-で] they [topic-は] long-time talked.
平和で自由な chains two な-adjectives: 平和 (peaceful) + で (connective form of だ) + 自由な (free). 雰囲気の中で is 'in the atmosphere of.' 長い間 is 'for a long time.' The sentence paints a scene of unhurried, liberated conversation.