Depends.

Part One:

Let's say you killed someone in English occupied France, for the sake of the argument in the 14th century.

To understand what the law is and how it's enforced, you need to know that everyone belongs somewhere. That's really important. Doesn't matter if you're living in a village or a city, if people know you, this might just be the one thing you need to survive.

So, let's say you killed someone and want to get out of Dodge. Might not be the wisest choice.

Every community has a tithing. It composes of theoretically ten men (if there are less, it's less. If there are more, it's more). Those men are responsible to watch each other, notice a crime and tell their constable or chief tithing-man. If they don't and it becomes public, they'll be fined. That being said, this is your first chance to get away with your crime. If you know one of them well enough, he might be inclined to look the other way. Maybe you need to bribe him. But it can work.

Second chance: You commited a crime, nobody notices. But some stranger went through your village just hours or a day ago. You can easily pin it on him. That guy is unknown, nobody knows about his story. And nobody will care. If he's accused and can't prove his innocence, there's a good chance he'll hang on the next tree after he's found. The constable may be bold enough to decide that. If your crime is noteworthy enough, it will be mentioned before the Sheriff who then will send out a manhunt. The moment they catch the alleged killer, they may just behead him where he was captured. No court of law needed. Nobody cares that he says he's innocent. That's what they all say.

So let's say, you are the killer, they saw you and the manhunt is searching for you. The rule is to hunt you, no matter what. You're a murderer. Only a church doorstep will hold them back. That's what the Statute of Winchester says, it's the law. You made it and reached a church. Now the up to 40 days of your asylum begin. Not more, most likely less. Those hunting you have to put a guard before the church. From 1315 on they're not allowed to starve you out, so they must give you food and water. But don't count on a dinner. It's most likely old bread and so on. You're allowed to leave the church for defecation, but that's it. Within those 40 days the local coroner should arrive and confiscate everything you own. Everything. You'll be naked. When you're lucky, he exiles you by giving you instructions to go to a port and take a ship to leave the country. And you'll reach that port.

But mostly, you won't be lucky. When the coroner can't be there in time, after 40 days they'll stop giving you food and water. You'll die of starvation (the law mentioned only needs them to feed you for 40 days). The other thing is the way to the port. You're naked, not armed. An easy target. And man, you killed one of their flock. Happy hiding. If they find you, you're dead.

If the coroner doesn't exile you, you're dead. Either you starve to death inside or the coroner will just hang you, plain and simple.

And then there is of course the fact that it's a common thing to just ignore church asylum. In 1320 a woman called Isabella de Bury kills a scriptor of Allhallows on the wall. She got pulled out of church and hanged. Also there is Richard Folville. He was a notorious criminal and a man of the cloth. When he was found in Westminster Abbey during a Merciless Parliament he was denied exile and the uncle of the king himself beat him out of the church and hung him.