'Coup' is a French origin loan word into English, as I'd say you are aware since you classified the question in 'French to English'. While the word 'coup' in the phrase 'counting coup' is still the same loan word from French as is used in 'coup d'etat', for example, the phrase 'counting coup' is of English origin.

couning coup

American Indians counted coup in combat. Touching the enemy with your spear or hatchet and that earned you points. Warriors had a coup stick which was decorated with feathers and scalps.

Counting coup was a battle practice of Native Americans of the Great Plains. A nonviolent demonstration of bravery, it consisted of touching an enemy warrior, with the hand or with a coup stick, then running away unharmed. Risk of injury or death was involved, should the other warrior respond violently. The phrase "counting coup" can also refer to the recounting of stories about battle exploits. It can also involve stealing items from the enemy. The term is of French origin from the verb couper, which means literally to cut, hit or strike. The expression can be seen as referring to "counting strikes". Coups were recorded by notches in the coup stick, or by feathers in the headdress of a warrior who was rewarded with feathers for an act of bravery. Counting coup was referred to in the Star Trek: The Next Generation first season episode, "Code of Honor".