In Norman England, Hunting of deer and boar in the UK was confined initially to the Royal Family and those whom they invited. It took place in "Royal Forests" which were areas where the quarry species were protected  by making it a serious offence to kill them there except as part of a "Royal Hunt". Later the privelege of "Hunting Forests"  was extended to notable land owners (Eg; Bishops). As early as the 13th century the Crown granted licences to hunt foxes and some crown servants were employed for the purpose. Eventually the laws protecting the quarry species became those covering trespass and poaching which applied on land  owned by anybody. Gradually Hunting in the UK was opened to Hunts (with  hounds) and stalking (with guns) for which Sports anybody can apply to take part. By the mid-16th century quite a number of private landowners had formed packs of foxhounds but Staghunting predominated. 

 In France, the Revolutionaries won the right in the Constitution for any  citizen to Hunt.  

In the 18th century  many factors were making Stag Hunting more restricted. Some Stag Hunts started to chase foxes and found that they  were worthy quarry. Furthermore, farmers well outside traditional Stag Hunting Areas welcomed Foxhunting as one method of helping to control  numbers of a significant "thief" of their possessions of lambs, chickens etc. Thus the Sport of Foxhunting spread until it covered much of the UK and acquired the dual purpose of sport and fox population  management. As Foxhunting grew in popularity it became better and better  regulated until it became the well disciplined sport we saw.