Gens d’arme is more correctly translated as ‘men at arms’, a term which was used in English. A squire was an apprentice knight, not merely a man at arms.
The OP is responding to the last paragraph of Why are the police called cops, pigs, or the fuzz?, a staff report dated May 31, 2005:
After archers, musketeers, and pikemen had spoiled the primacy of mounted knights, “man at arms” could simply mean “knight, but mounted infantry rather than cavalry”.
The gendarmes don’t belong to the police (even if it’s a police force). They belong to the army.
The French Gendarmerie nationale are still administratively part of the army (and provide the army’s Military Police) but, since 2009, report operationally to the Minister of the Interior, like the Police Nationale.
Canada’s national police force, the Royal Canadian Mounted Police become le Gendarmerie royale du Canada in French, in reference to the historical origin of gendarmes as mounted police units.