Obviously 'Europe' is a big area and 'Medieval' quite a long time period, but do we have any evidence of a fantasy-style City Watch whose purpose was mainly law enforcement and defence of the city at any point anywhere? I have seen some say that law enforcement as we know it (that is to say, not just the military being used to keep the peace) is a relatively new thing and yet the idea of a City Watch seems quite ubiquitous. For reference in Medieval Fantasy I'm thinking of, say, the Gold Cloaks from GoT or the Night's Watch from Discworld.
Always more to be said, but do check out this answer from a similar question, done by /u/gadarn.