Where does “cour” come from?

I need to work through this carefully, as there are some issues with the chain provided. The chain shows: - Japanese クール - English cool - French courir - Proto-Indo-European gel- - (repeated gel- four more times) There's a clear problem: French "courir" (to run) does not etymologically connect to English "cool" or to the PIE root "gel-" (which relates to cold/freeze). This chain appears corrupted or nonsensical. Additionally, you've asked me to write about the headword "cour (English)" but "cour" is French for "court," not an English word. The English word "cool" is in the chain, but not "cour." Given these contradictions, I cannot write an accurate one-sentence etymology summary. The chain is internally inconsistent (courir doesn't lead to cool), and the headword designation doesn

cour (English): A three-month unit of television broadcasting,...