I am working with a fantasy setting wherein a society of feudal humans launches a crusade against a continent largely controlled by elves. Though the human society is not entirely without its own magical resources, the primary source of its military strength is in fielding large numbers of heavily armored Knights. It's basically late 14th century France, with bad infantry and mediocre skirmishers.
The Elves in this setting are on their home turf and have large numbers of truly top notch skirmishers in the form of crossbow wielding marksmen and mounted archers.
What would be the best way for the humans to go about combating a force such as this? I know that guerilla campaigns are frequently unsuccessful, but most of the information I can find about combating such tactics are for modern armies. How would a medieval army go about suppressing a force of determined guerillas?
Edit I have been asked for a fuller explanation of the scenario several times now, so here goes.
The situation: A large feudal nation of humans has launched a crusade against a distant continent ruled by hostile elves. These elves have operated like the Barbary Pirates since time out of mind and a variety of factors have finally motivated the humans to attempt to put a stop to all this raiding and slaving. The crusaders aim to devastate the elvish homeland, raze one of their major cities, destroy their naval power and rescue enslaved citizens.
To this end the King of the human nation has declared a crusade. All major lords of his nation are expected to send forces if not attend themselves. Due to his prestige and widespread sympathy for this cause independent knights from various foreign powers have also joined, inflating the proportion of knights vs footmen in the crusading army.
The voyage from the human continent to the elvish is quite long, and can take from a month to a month and half depending on weather.
On a neighboring continent to the hostile elves, about a week to a week and a half away, a nation of far more friendly elves exists. Though they are not sending troops, they approve of the cause and have agreed to sell them supplies at discount, provide aid at sea and grant them certan guides. These other elves will not allow them to land on their continent however. Hence their supply lines are shorter than their reinforcment lines.
Neither side is willing to negotiate with the other in any meaningful way.
The Land: A long narrow continent in the northern hemisphere. It is relatively small in the south, 100 -150 miles across, fanning out into a wide land further north till it hits polar ice. Much of it is a rocky wasteland, though coniferous forests run up and down the center of the continent. Between these and the mountains the land is quite rugged. The besieged city in question lies roughly in the center of this southern portion about 50 miles inland from where the crusaders have landed. This is the southernmost city of the elves and is relatively isolated, cut off by mountain ranges from the others. It sits in the middle of the forest on the shore of a lake, which, by various rivers leads eventually to the sea.
The Forces: The Humans are a picture of 13th-14th century France with some magical elements. I will leave those out for the most part as they are rare enough to not dramatically impact the strategic picture.
Human Knights clad in plate and chain with heavily barded warhorses comprise the prime force of the nation. In one of the few widely available magical things they have going for them, their horses interbred with magical elven steeds in the past. They are larger on average than horses in real life, and can wear heavier armor while maintaining their stamina. Imagine that 4 out of 5 knights in the army is riding an abnormally intelligent Destrier the size of War Admiral. The foreign men at arms ride more normal Courcers and the like.
Accompanying the Knights and Men at Arms are an assortment of poorly trained peasant soldiers. They are accustomed to being deployed in battle to a static location, holding that area and letting the knights do most of the work. They are supported by longbowmen, who are quite good, but average out to mediocre in a fantasy setting. Around 1000 professional soldiers have come with the foreign knights, giving a little bit of backbone to the infantry.
Of finnal note on the humans I will mention something about their higher nobles. A very small number of the knights and higher Nobles in the army, including the King, have extended lifespans and superpowers a la Arthurian Legend/Orlando Furioso. Assassinating or sniping the highest leadership of the army is a dubious prospect at best even for the elves. At the highest levels of command the Peers of the King have supernatural levels of military experience. The King is around 130 years old, with some of the Peers being in the 200 to 300 year range.
The Elves in this setting are basically good at everything, but suffer from low numbers. They have superior infantry, cavalry, archers, the works, but not in high enough numbers to drive the crusade from the field in a single hammerblow unless conditions were optimal.
Their citizen militia, which is the bulk of their forces, is competitive with professional human soldiers, and they have large numbers of very good crossbowmen and horse archers.
The elvish professional soldiers are equipped with nearly weightless armor of similar strength to heavy steel plate. They have a full range of weaponry but prefer swords for close shipboard combat.
Elvish heavy cavalry are superior to human knights, riding the elvish steeds that the human steeds originally mixed with to become what they are now. Again however, there are so few that they would be quickly overwhelmed in most massed cavalry engagements.
The Numbers: I do not have concrete numbers for the forces involved here, however the nation is larger than France and like in the real crusades forces from multiple neighboring countries have arrived to assist. I will say 25,000 Men at Arms, and 80,000 Footmen. Lets then add in another 40,000 for workers, sailors, woodsmen, grooms ect.
The Elves are a bit trickier, they are on their home turf, but suffer from a low population compared to humans. Although their citizens can almost all fight, they cant mobilize all of them for obvious reasons. They also have a huge slave population which they have to keep under heavy guard at all times, especially when they are under siege. A slave revolt from within is to be expected at some point, but we will assume that it is suppressed with minimal elvish casualties.
Let's say a population of 300,000 elves of fighting age in the city and surrounding countryside. A fifth of those can be mobilized directly against the invaders. 20,000 within the city, 40,000 without.
Of these 60,000 lets say 10,000 are professional soldiers, the rest are citizen militia, generally superior to the human footmen, but inferior to knights. Lets put their cavalry force at 5,000 horse archers, and 1500 elvish knights.