In medieval warfare, what sort of fighting went on that a king was not personally involved in or at the head of? For the sake of curiosity, people with any specialty can feel free to answer, and I would like to know about whatever chronological or geographical range you are willing to discuss, although personally my main interest is in the first half of the Hundred Years War.
So how often (during the reign of Edward III in particular) would there be offensive fighting when the king was engaged elsewhere? How large might an engagement be? Were they limited to skirmishes, or were there any recorded sieges not headed by a king (or the Black Prince)? Would siege equipment be used, or did the expertise and resources involved in constructing siege weapons limit its use to major conflicts only? Could a smaller "side-battle" have trebuchets as well?
Who else might head an attack? A duke, a count, a knight-captain?
I have spend a lot of time learning about the early campaigns of the Hundred Years War (from the English perspective especially), but almost all information I have has tracked Edward or his son personally, and I would like to know what other fighting might have been going on at the time.

I ask this largely out of curiosity, but more selfishly because I am writing a historical fiction set during this time (1340-1350) from the point of view of an English knight and I want to know if it would be acceptable to “invent” fictional battles for him to participate in outside of the main historical campaign or if to be realistic he would have to follow the king throughout his time in France.

During the Hundred Years War, there were quite a few small feuds between nobles in France. There was an interesting academic article published this year on your very subject. You can find it online here: http://www.medievalists.net/2010/03/08/techni...h-century/.

See also Howard Kaminsky, "The Noble Feud in the Later Middle Ages," Past and Present 177 (2002), pp. 55-83.

In addition to feuds among various French noble families (which undoubtedly made it difficult for them to defeat the English early in the war), there were the chevauchees mounted by various English commanders. Edward III may have led some. The Black Prince did lead others and I think a few other dukes/barons/maybe the Black Prince's brother led some others.

Adding into the mix where instances (perhaps earlier in the war) where the French would seize English lands as retaliation for Edward III's issues in giving the kind of homage France wanted; England would try to get them back. And some of the lands on or near the border between English-held lands and French-held territory may have been skirmished over.

I'd read up on the Hundred Years War in a little more depth if I were you. I think there are opportunities to find historical events that would fit your fictional scenario.

I'm away from my sources at the moment, so I'm afraid I can't give you anything more concrete right now.

Speaking of the 100 years war, Froissart's chronicles are, besides perhaps one of our main sources from this era, well worth reading (if you can find a good translation).

Look up the Battle of Neville's Cross 1346. While Edward III was in France with the main portion of the English Army David II invaded northern England. (actually turned out to be a big mistake for David). Suffice to say the King could only be in one place at a time. tr

PS The Breton War of Succession is a fertile ground of many smaller battles not necessarily involving Edward III directly and was used by Bernard Cornwell in his Grail Quest Novels, the Battle of La Roche-Derrien in particular

If you're writing historical fiction, then it'd be usually a good idea to pick small-scale actions where your character's individual exploits wouldn't be submerged by the sheer scale of the battle--and there was certainly no shortage of such actions led by non-royal personages, especially since small raids and scouting expeditions were often made at the initiative of the local commander without the need (or desire) to consult the distant authority of the King. I'd second the recommendation for Froissart, but I'd also add De Re Militari's collection of translated primary sources:

http://www.deremilitari.org/resources/articles/sources.htm

One of the instances that might be particularly relevant to your question is http://www.deremilitari.org/resources/sources/peasantsfrance.htm

That's great to know. I suspected there were other goings-on, but most surface research covers royals nearly exclusively. Clearly there was another aspect of war during this period. I was not aware that it actually had its own name (seigneurial warfare, according to the article from medievalists.net) I have done a fair bit of research on the Hundred Years War but it seems my sources were too generic. And here, primary sources come to save me yet again. Thank you everybody.
I hoped to be able to avoid tailing Edward's army in my story as it would indeed drown out the significance of the protagonist and likely be nothing more than an overly flexible, creatively written history book rather than a novel.
Mercenary work in particular seems to fit under the net of those who fought with or without a king present.

Historians also sometimes call non-royal wars "private war".

Due to the nature of communications in a pre-telegraph world, leadership was often done by mandate. The king would give a task to a commander, and send him of, after which he was efficiently on his own. such a task could be everything from buying provision to "Force the nobles of region x into submission, by means of the troops I hereby authorise you to levy from the fiefs Y and Z".
Since the lack of communications hinder direct control or support, a such expedition would efficiently be on their own.

Other than that, certain nobles, spesifically marquises, (a marquise is a count who has a fief on the borders of the realm, and thus have extra priviledges) where authorized to raise troops on their own, or might do so in pure self defence or oportunism.