Some historians agree that hunting, when practiced by nobles and aristocrats, was a mixture of politics and genuine sportsmanship. When practiced by memebers of the lower classes, it was more of a trade or substinence activity heavily regulated in its performance. Such restrictions were quite varied as they depended mostly on the region and single lordships which possessed the legal power (or simply made so) to use forested areas for hunting. I do not possess an actual legal statute to present you, but I have studied a litigation between an Italian noble and a village over the hunting rights of migratory ducks from around the early XV century.

What we are convinced about is that deer hunting and hunting with birds of prey was a prerogative of aristocrats only. Deers and stags were seemingly renowned as animals of royalty with attributes fitting the higher layers of society, and do figure in many illustrations of the period. Hunting with birds such as falcons, hawks and other predatory birds required great skill and great wealth as they were fragile and very hard to train beasts. To the point that Holy Roman Emperor Frederick II (1194-1250) authored a treaty: "De Ars Venandi cum Avibus", "On the Art of Hunting with Birds".

Hunts could last several days and were performed mostly on horseback. This ivory plaque from maybe around 1350 ca. shows a group of men on horse, accompanied by another other figure on foot which could have been the dog handler, blowing a horn while the dogs bite and chase a stag. One of the men has a falcon resting on his left forearm which looks to be padded (the same reinforced glove you might see worn by modern falconers at reenactment events). Another man is holding a bow and two others are hitting the deer with swords. Perhaps this scene depicts the whole hunting process, from when the party first sets out up until the preys are found, already attacked and wounded by the dogs, and the hunters finish them off. Although I reckon that the usage of swords in this way might be due to artistic preference, most of it shows a plausible hunting scene.

This illustration from a manuscript dated between 1300-1340 ca. shows us instead two men hunting a boar. One has climbed up a tree and is armed with a spear, while the aristocrat on horseback is hitting the boar with a sword, helped by his dogs and another man which is stabbing the beast with what looks like a knife. There is a theory which states that lower classes could hunt boars by ambushing them from the above, jumping down and stabbing them with a spear. Spears which are carried by noblemen as well in this other illustration and used to attack a prey which unfortunately "didn't fit into shot". Lastly, birds were used to hunt small preys (rabbits and such) but also other birds. This miniature, however, shows a man shooting a crossbow aimed at a tree full of birds, some of which look like magpies, others resembling quails, and the top one looking like a bird of prey, perhaps a hawk.

I hope this answer helps you.