In my world, there is a zombie infestation that destroys and takes out many kingdoms, citystates, and villages. These zombies are fast and like the ones from zombieland. It is possible to get cured, but you would need serious medical care, and the survival chances are low. The technological state is similar to that of the 16th-17th centuries. Most of the major cities have tall walls, and those that haven't are trying to build them fast before it spreads. At first, they think it is just a normal medieval disease. Now at this moment, the zombie infection begins. How would a kingdom or civilization at a time period like this survive, mainly the 17th centuy? Note: while the fantasy world has multiple continents and different cultures, the main focus here are the european-like kingdoms and civilizations.
The survival of such areas will depend on low population regions blocking the movement of people. Even in well-developed regions of the world at this time, there will be significant regions of wilderness and tiny isolated villages. When people become concerned about zombies, they will withdraw to old fortified places with many of the people available. Ruthless rulers will slaughter populations to make breaks ( ironically driving people into more isolated places and improving those peoples odds of surviving).
Transportation in this time is more primitive and slow, so such a disease might have a lower chance of crossing long distances. So spread will be much more local and dependent on local circumstances. Island nations would fare better, but drifting ships might still provide a route for infection.
Technology might work in their favor if armor is still available. I suspect a suit if chain mail or boiled leather might be a fairly effective protection. And melee weapons have often been portrayed as being more effective against zombies than guns.
But if the zombies can have a carrier (like rats) or if the zombies wander long distances and persist for long periods in a region, there will be little they can do to keep them from slowly grinding them down.
Fall Back in Technology
It turns out, 14th and 15th century military technology was pretty well-suited to a zombie outbreak. The standard infantryman wore a solid suit of steel covering, that would foil zombie teeth; and utilized polearms, ideal for keeping the undead out of arms reach; or pinning the living dead in place.
11th and 12th century soldiers were in even better spot, wearing similarly impenetrable armor as an outer layer. Beneath which, padded gambesons are also the equivalent to modern "bite proof" suits of dog trainers.
The stuff, you can see here, is pretty much undefeatable. It took the development of specialty anti-chainmail weapons to beat chainmail, and it took the invention of the cannon (note the cannon, not the rifle) to beat plate mail.
Unfortunately, the 16th century medieval soldier has laid aside much of that protection because the cannon has rendered it obsolete for nation-to-nation warfare.
However, the industrial processes exist, and being only a hundred years old, it would not be too much of a stretch that families dug grandpa's mail out of a locker for the zombie apocalypse.
River by river.
Here is Ukraine. Like the rest of Europe it has plentiful rivers. The good thing about zombies of the Zombieland or movie WWZ variety is that they go zombie in a hurry and then they are unsubtle - they do not hide and there is no secret zombie reservoir of infected persons.
Even small rivers present nearly impassable barriers to zombies. Zombies will not drown but a zombie in the water will fill internal body spaces and sink. They will then be moved by currents to low spots. These low spots are muddy and pitch black - zombies will not be able to get traction against the bottom and so will accumulate. Depending on zombie buoyancy they might sink further, into the mud.
Your villagers will clear land spaces river to river by moving through the countryside ringing bells and calling out "зомбі? зомбі?". They will have their farm implements with them and also dogs. Zombies will be attracted to these parties and be dispatched by phlegmatic country people. Dogs will bark at any zombies that show up at farms at night, and people will go out and dispatch them. These will be numerous, small dogs who require little food but have powerful and persistent barks.
Uncleared regions will harbor zombies. Unmanned zombie traps with windpowered noisemakers will be erected in these territories to lure zombies into quarries or rivers. Bridges will have V shaped walls erected such that zombies coming to the bridge will move laterally along the walls, which end at a gap in the railing. Nonzombie refugees from these areas will come across bridges and not be fooled by the V walls, or be ferried across by persons in boats or manned ferries. These refugees will be welcome manpower in the cleared areas, where the population has diminished because of the zombie epidemic.