Europe is a very large area.
In the early middle ages Europe contained many provinces ruled by the eastern section of the genuine original Roman Empire, what is usually called the "Byzantine" Empire.
So the "Byzantine" Empire certainly had units of totally professional soldiers.
But it may also have had semi professional soldiers in the theme system. I have the impression that the theme soldiers held farmland through military service and had to serve in the theme army when called to active duty. Thus they were part time soldiers like militia, national guard members or army reservists in the contemporary USA. I am not entirely certain that is the contemporary understanding of the theme system but f i fitif it isn't it can be corrected.
And I don't think that all medieval knights all over Europe all during the millennium that the Middle Ages lasted for were always professional soldiers.
Knights and men at arms who resided in the castle of their lord as part of his retinue were professional soldiers who worked for their lord for room and board and maybe cash pay.
But it seems to me that a knight who had a manor and was the lord of the manor would usually hold the manor as a fief from a higher lord. Thus he would administer his manor full time but would have to serve in his lord's army a specified number of days per year and fulfill other duties specified in his feudal agreement. Thus knights who had manors were part time warriors like militia, national guard, or army reservists in the USA.
And I suspect that a number of medieval societies had social classes vaguely similar to knights and thus being semi professional part time warriors.