The music video for "New Moon on Monday" was filmed by director Brian Grant during the morning of December 7, 1983, in the village of Noyers in France. It has a loosely sketched storyline in which the band appear as members of an underground resistance movement called "La Luna" (the name is one of the few connections between the video's content and the song lyrics), organizing a revolt against a modern (1980s-era computers are used) oppressive militaristic regime, apparently in France.