Bevore anyone says something, a disclaimer: yes, I know the medieval period was immensely long and that what was true for the 1300s was not necessarily true for the 800s.
Now my question is this: did the news about the biggest and most important battles fought in Europe make its way around the entire continent? Would Władysław Jagiełło have heard about the battle of Agincourt? And vice versa, would Henry IV have heard about the battle of Grunwald*? Would the news of the Siege of Baghdad in 1258 (not really Europe, I know) have reached Castile and Italy?
As you already pointed out yourself, your question is very broad both geographically as chronologically. You have to ask yourself a few questions first :
Most of our knowledge stems from written documents. Most important battles are mentioned in literature. It's also possible to reconstruct and examine these battles through more practical documents, but these kind of documents weren't that common in early medieval times. A lot of our information thus stems from literary documents. However, these literary documents were often produced for a very specific audience and weren't overly concerned with fact-checking.
It's important to note that most medieval societies were still heavily defined by an extensive oral tradition. While we can't underestimate the effectiveness of this oral tradition, it's very difficult to accuratly gauge how extensive it was. So news mostly spread, even before being written down, through word of mouth. Knowing this, we can potentially estimate how "connected" a certain region or court was. The more central and trade-heavy regions would have had a larger influx of exotic news, unlike the more isolated and self-sufficient regions.
Remember that this obsession with news is a more recent thing. A lot of people were illiterate and disconnected from the rest of the world. Mostly the urbanized elite or nobility would actually care about "worldly events". That being said, this news could potentially spread to even the most illiterate person through word of mouth which was -again- very much part of medieval society.
Knowing all these limitations, it should come as no surprise that news spread fairly slowly. So naturally most sources will only mention remote events which happened some time ago. However, in the later medieval times when there was more economic interaction and better travel infrastructure, news traveled relatively fast through the European continent. Most literary sources or books would have had a limited audience and were written long after the events, so it's difficult to gauge when they first heard of the event they mention. In the later years of medieval times there are other some documents that were concerned with bringing "news". Pamphlets featured a wide variety of subjects, but the mention of distant wars or extraordinary events were common. Some almanacs would also try and provide a list of noteworthy events in the past few years, this became more common in early modern times.
As I know, the Canterbury Tales were written during the Hundred Years' War.