Word Detective says "...The word "police" itself, however, has ancient roots. The Greek "polis" means "city," and, in addition to being the ultimate source of "police," gave us "politics" and "policy." The Latin derivative "politia" meant "civil administration," and eventually produced the French word "police," which English adopted in the 16th century. The similar words in other European languages that you mention are products of the same process.
When "police" first came into use in English in the 16th century, it was used to mean "public policy," "civil administration" or "civilization" in general. Edmund Burke illustrated this sense in a rather negative way in 1791, caustically describing the Turks as "A barbarous nation, with a barbarous neglect of police, fatal to the human race," by which he meant insufficient civic cohesion and order, not simply a lack of cops. On the other hand, one entomologist of the day considered ants to have plenty of this kind of "police," describing them in 1820 as "[t]hese insects, whose faculties, police, and sagacity have been, by some authors ... not duly appreciated."
Gradually the meaning of "police" shifted toward the enforcement of laws and regulations to preserve public order, and by the early 1700s "police" was being used to mean a specific governmental department or force charged with law enforcement. But only at the end of the 18th century, with the organization of the first civil police force, London's Marine Police in 1798, did "police" acquire its modern meaning of "professional civil (as opposed to military) force for law enforcement."