Well... define "innocent."

I can only really speak with any degree of expertise on the Hundred Years War, so I'll confine my answer to that scope. But I think it's important to acknowledge that military violence against civilians was definitely a topic being discussed and debated at that time, most notably from a clerical perspective. I'll make several references here to Honore Bonet's The Tree of Battles (1381 or thereabouts), as it's a book that directly addresses this topic and was written by a cleric for a noble audience.

But essentially, principals of military conflict in the Hundred Years War were such that attacking illegitimate targets of violence was generally condemned. What constituted a legitimate target was, however, the subject of some debate. The "commonplace" military thought process was more or less as follows: By paying taxes (in terms of food or coin or what have you) to the opposing political structure, the peasants were therefore directly supporting the ability of the enemy to directly wage war, and therefore inflicting violence against them (and, more relevantly, taking their stuff) was justified. This was, of course, a rather pragmatic position (it's a lot easier to feed an army when you can forage off the land), as well as one with underlying significance as a challenge to the feudal order of the enemy (if lords can't defend their peasants, then they're failing to adhere to a principal responsibility in the late medieval social contract).

Of course, it should be no surprise that Honore Bonet and other clerics and writers (such as Christine de Pizan in her 1415 Book of Deeds of Arms and Chivalry, which draws heavily from Bonet) did not approve of these justifications. One of the most fascinating parts of The Tree of Battles is how Bonet lays out a variety of different situations where violence against apparent noncombatants might or might not be allowed. Can soldiers take an old man long past fighting years captive? (No, unless he's an important advisor for the enemy). Can violence be inflicted upon priests? (No, so long as they're living up to their obligations and not acting as combatants themselves, *and they're allowed to defend themselves against unjust violence without counting as combatants or violating their responsibilities as priests). And so on, and so forth.

The question that this begs is, of course, if Bonet's recommendations and others like them were ever actually followed. Well... that might be less likely. Generally speaking, military necessity was decidedly on the side of the looting and the pillaging, provided all the legal preconditions lined up.

And that's a very important "provided". I don't want to get too much into Just War Theory in this response, but remember when I mentioned earlier that the fact that civilians and peasants were actively paying tax to an opposing governmental structure was a critical element of the justification? Well, for that, you require a legitimate opposition, which means you need a just cause of war against the crown. And you can't conduct a legitimate private war against the king just on your lonesome, you essentially need to be working for another king who has a legitimate cause of war. There are accounts of the English looting and burning through the French countryside one day, only to start paying fair price for goods seized the very next day, after news came that a truce had been signed. And legitimate war was a legally enforced concept - in his The Laws of War in the Middle Ages, Maurice Keen describes accounts of a trial of a notorious mercenary. He had served the English for a time, lording over a bit of seized territory in France and extracting "taxation" from the local countryside, but when a truce was signed he maintained the same behavior. A halfhearted defense that he had changed his allegiance and now supported the King of Navarre in his war against the French crown was submitted in court, tried, and found lacking, and the mercenary was put to death.

So, to answer your original question, the best I can say is this:

Some noblemen probably did express regret, sympathy, or disgust at the demise of noncombatants during the Hundred Years War. They were human, after all. But fundamentally, in a war between princes, those noncombatants about which you ask were considered legitimate targets for physical violence - "caught in the middle" wouldn't be an accurate descriptor for their plight. The accounts that survive bemoaning the injustices inflicted upon them were not noble in origin, though they were intended for a noble audience and seem to have been read and enjoyed by nobles. And cases of violence being committed against targets that were universally considered to be illegitimate targets - peacefully serving prisoners, for example, at no risk of escape - there would have been significant social condemnation.

Primary Sources:

Bonet, Honore. The Tree of Battles. Translated by G. W. Coopland. Cambridge: Harvard University, 1949.

Froissart, John. The Chronicles of England, France, and Spain. Translated by Thomas Jones. London: William Smith, 1839.

de Pizan, Christine. The Book of Deeds of Arms and Chivalry. Translated by Sumner Willard. University Park: University of Pennsylvania, 1999.

de Venette, Jean. The Chronicle of Jean de Venette. Translated by Jean Birdsall. Edited by Richard A. Newhall. New York: Columbia University, 1953.

Secondary Sources:

Allmand, C. T. The Hundred Years War: England and France at War c. 1300-1450. Cambridge University, 1988.

Contamine, Philippe. War in the Middle Ages. Translated by Michael Jones. New York: Basil, 1984.

Keen, M. H. Chivalry. New Haven: University of Yale, 1984.

Keen, M. H. The Laws of War in the Late Middle Ages. Toronto: University of Toronto, 1965.

Sumption, Jonathan. The Hundred Years War. 3 vols. Philadelphia: University of Pennsylvania, 1991.

Synan, Edward A. "St. Thomas Aquinas and the profession of arms." Mediaeval Studies 50 (1988): 404-437.

Reichberg, Gregory M. "Thomas Aquinas on Military Prudence." Journal of Military Ethics 9 (2010): 262-275.

Wright, Nicholas. Knights and Peasants: the Hundred Years War in the French Countryside. Suffolk: Woodbridge, 1998.

As a follow up question: How often or common was the justification of the human cost of these conflicts for the leaders involved the "injustices" suffered at the hands of the other side? How often or common was it said that the actions of one side were only necessary to defend against the other?