I'm confused about the use of "levies" and the use of professional soldiers in general. Did the armies, between 1066-1453, really mostly consist of armed peasants? Or is this a misconception?
To what degree would those armies be "professionally" organised? Not only in tactical terms but also in logistics. Was there any sort of top down planning to make sure that all the soldiers were properly equipped and to make sure soldiers fought as a unit instead of individually? Or did this only start in the renaissance?
(BTW If Western Europe is too broad then please focus on England and France)
Your year range is extremely broad, but I understand what you're trying to say.
The idea that armies consisted of armed peasants is not every correct, at least not for the time period you're speaking of. By the time of the norman invasion of england (1066), the feudal system was well under way in france, and this influenced the way that wars were fought. For example, if the king of france were to go to war, he would call upon his most powerful vassals to supply him with troops (in most cases a duke or at least a very powerful count or baron). Those dukes in turn would call upon nobles in their lands, which would in turn call upon their men at arms. So you see, there was an expectation for the warrior class to supply their lords with trained men(in most cases knights) that were ready to fight wars. Of course, this system depended on how much the french vassals liked the king and could fall apart at if there was a weak king in power (as it did many times.).
Now, this was fairly similar in england, especially earlier in this timeline. However, moving towards the 1300's, the king of england, Edward iii, found that there was a shortage of warrior class nobles able and willing to fight for him. And since he needed an assload of men to help him win lands in france, he began the tradition of making archery a mandatory sport for even the common folk. He developed a warrior culture even within the lower classes of society, thus establishing a base of trained men loyal to england as a whole. And since Edward was the king of england, they supported him. This later developed into the yeoman class (an early middle class), and helped many later english monarchs defeat armies of french nobles, much to the dismay of the french, as they felt their knightly men were supperior to the english low class longbowmen.
Long story short, the french got really sick of being defeated over and over again by the english "peasant armies," (particularly at the battle of Agincourt where a much larger french army consisting mostly of knights was utterly defeated by the english army led by Henry V) and decided to shift focus from a mostly knightly army to an army consisting of trained men. This eventually led to the development of professional armies in both england and france, and this idea soon spread throughout Europe.
I hope this answered your question more or less! If you need a source let me know, it might take a bit to find some of my books lol