From the liner notes

A hidden gem of 1960s New French Cinema, Alain Cavalier’s Le Combat dans l’île is as coolly modern as it is tensely gripping. Filled with thrilling plot twists, jazzy gun battles and stormy betrayals, this scintillating neo-noir unfolds against a backdrop of ’60s political turmoil and is strikingly shot in stark black and white by legendary cinematographer Pierre Lhomme (Army of Shadows, The Mother and the Whore).

The charismatic, surly son of a wealthy industrialist, Clément (Jean-Louis Trintignant, of Z and The Conformist) leads a double life as a member of a right-wing extremist organization. When he’s ratted out after a failed assassination attempt on a prominent politician, Clément and his long-suffering wife Anne (the luminous German screen siren Romy Schneider) flee Paris to the idyllic country home of his childhood friend, pacifist print-maker Paul (Henri Serre, of Jules and Jim). As affection blossoms between Paul and Anne, the emotional as well as political tensions soar—and eventually explode.