Basically I'm wondering about the relationship between ethnicity, language, politics, etc. Was someone born in the Angevin lands in what's now modern France, speaking a southern dialect, and fighting for the King of England, considered French or English? Or maybe he was considered French by some and English by others? Similarly someone from Calais and Normandy. Or did people describe people in more complex ways? Were the French very aware that Welshmen were different from Englishmen (and in fact, how different were they?)/
Two blokes in a pub, talking about Brexit:
"Do you remember the good old days?"
"What good old days?"
"When we could cross the Channel and plunder France."
"What are you talking about? We weren't there!"
***
[Part 1]
A few years ago Stephen Clarke published a very funny book called 1000 Years of Annoying the French. Though it is highly entertaining and generally well informed, it is built upon a shaky foundation. It relies on the tacit concept of "usness" (better known as "wirheit" in German). What the book is saying is that "We, the English, have been annoying them, the French, for over a thousand years."
The concept of usness is widely spread in 19th century history books. Medievalists were often looking for the "origin" of their nation. When did it all start? What did we go through? What does it mean to be English, or French, or German, or else? They tracked down old chronicles and literary texts. More often than not it underlined the idea that there was some truth beneath anyone's nationality. "Oh, you're French? Well, considering the history of your people, you must be like this." Past victories were a matter of contemporary pride.
The best history books didn't fall into those pitfalls. Knowledgeable historians knew that those who were called "English" and "French" in medieval chronicles, for example, were very different from them, if not completely foreign. They knew that the concept of usness was a delusion.
Let's consider the "fall of Rome" for a second. When Petrarch thought about it, he dated it to the rise of "foreign" dynasties on the imperial throne. When Nerva ascended to power in 96 AD, that's when it all dived into darkness. Modern historiography argues that the fall of Rome happened in 476 AD. However, I'm sure that if we asked Cato the Elder, he'd have a very different opinion on the matter.
What defines the long term continuity of a set group of people? Is it moral values? Is it cultural customs? Is it the use of a language? Is it territorial belonging? Is it institutions? I will not delve into this heavy debate here but it needs to be considered that just because people then and people now are called with the same word, it doesn't mean that they are part of a continuous history. We could honestly research "What defines Englishness?" at different point in time and we'd come up with widely different answers for every generation of people who called themselves "English". The same with the French, the Germans, etc.
The search for national identity through historical constant features remains well alive today. It is even broadcasted on national television. Robert Bartlett's BBC documentary about the Plantagenets (now available on YouTube) indulges into such considerations. I should seriously watch them again and count how many times he says "to this day" to emphasize the importance of a historical event and how it is still shaping our present structures and institutions. He's the first to admit, though, that at first the Magna Carta was a resounding failure. It only picked up many years later to assuage subsequent political dissensions.
Robert Bartlett also starts by making an interesting point. The Plantagenets never called themselves as such. We call them that way. It makes it more easy for us contemporary historians to encompass a period of English history and understand it as a whole. We have the very same problem with the Tudors. We call them Tudors, we talk about the "House of Tudor" but there was no such things for Henry VII and his heirs.
My point is that historians work with labels. It makes their job easier. We've been knowing for a long time now that the expression "Middle Ages" wasn't ideal. However, we keep working with it. We keep talking about a "medieval era" that eurocentrically spans from 476 to 1453, as if people who lived one millenia from each other belonged in the same basket.
The Hundred Years War is said to start in 1337 and to finish in 1453. Technically, however, it only ended in 1475 when both kings of France and England signed a peace treaty in Picquigny.
The fact that we call it the Hundred Years War implies that it unfolded as a continuous "main event" though this was not the case. The Hundred Years War is easily seen as a clash of nations, England versus France, but again, things are not that simple.
If anything, the Hundred Years War was a very long period of intermittent French civil war. The king of England was a French noble himself. And when I say French, Edward III who started the whole thing had an actual French princess as mother and he owned several fiefs that were tied to the French crown. He spoke French, so did the English kings who succeeded him. The English Parliament was still held in French when the Hundred Years War broke out and English laws were written, also, in French, until Henry V rose to the throne. Though he was the king of England, Edward III was pretty much a French vassal, and England was his personal piggy bank.
I mean, John the Blind (Edward III's contemporary) did nothing different. He was technically bound to the Holy Roman Empire as the count of Luxemburg. However, he was culturally French (spoke French, attended the French court, the king of France was a personal friend, he had French poets following him around...). Moreover, John the Blind was king of Bohemia but he barely ruled that realm personnally--he left his son to do it for him. Meanwhile, he mostly visited the Bohemia when he was in need of money, which still angers Czech historians today. You could be king of a country yet belong to another culture entirely. It is even safe to say that medieval aristocrats such as kings and mighty dukes were "above" any kind of national feeling. I personnaly did some research on Charles IV of the Holy Roman Empire sense of identity by reading his autobiography closely and what do we find? He's a Christian. Hurray! Nothing else. Considerations of national identity totally fly over his head.
So, even as I'm saying that Edward III was "French" we need to understand that even "being French" was not even a thing as it is today back then. By the middle of the 15th century, Robert Blondel started to argue (in Latin) about the differences between the English and the French "races". He goes as far as to call the French "Gauls". The ideological foundations of nationalism certainly find their roots in the 14th and 15th century but as to argue that nobles felt "French" or "English" or "German" would be a stretch, especially since there are many ranks within the late medieval nobility. We need to differenciate the noblemen that felt like they belonged to a "country" and those who couldn't indulge into such consideration because they inherited and purchased lands all over Christendom.
What is the Hundred Years War? Is it a clash of nations, really? Edward III was maybe "French", so to speak, and we could therefore argue that it was nothing but an extended period of intermittent civil war. However, what about the people who fought for him? What about the soldiers? Did they feel like they fought for a national cause?
Whatever the answer to that question is, needless is to agree on the fact that the Hundred Years War wasn't one continuous war but a long series of sporadic conflicts and that it didn't only involve the English on one side and the French on the other. The Scots, the Spanish, the nobility of the Holy Roman Empire, they all joined in on the fun. Moreover, the French slaughtered each other just fine without the help of "foreign" (what ever that is) intervention.
Let's try to untangle those many webs in part 2.
So, this is a pretty complex question, and I'm going to split it up into some more manageable chunks, but let me know if there's something that I've missed. Also, I'm going to restrict my answer to the first phase of the war, up to 1360, because thats the period I know closest, and I'm not entirely confident of being able to give a comprehensive answer that included the shifts in French identity in the later stages of the war.
Before we do start though, I want to make a distinction between Northern France, Southern France, Brittany and Flanders. These were all part of the Kingdom of France, but were almost completely different, in terms of cultural, linguistics and legal systems. Within Northern and Southern France there was also a huge amount of differences in each province, and although it is possible to roughly make this division because of a difference in dialects I want to reinforce just how little similarities someone from the Langeudoc would have with someone from Saintonge, despite both being 'Southern' places.
How 'English' would someone from Calais be considered?
I'm starting off with the easy part. They were English. After the capture of Calais in 1347 the vast majority of the citizens were expelled and replaced by English, mostly soldiers, although the government gave grants to traders who would move there. For a long time, Calais was a military colony, with its only purpose being to supply English armies who may land there.
How 'English' would someone from Normandy be considered?
Again, this is quite simple. They weren't English. By the start of the war Normandy had been controlled by the French kings for over 100 years, and the Dukedom was often given to the Dauphin in the same way that Wales was ruled by the Prince of Wales. However, they weren't exactly thought of as 'French', mostly because that kind of national identity only really existed for the aristocracy at this point of time in France, and even then, its extent varied hugely across France. Something to note though is how much of a contribution Normandy made to the Hundred Years War. They usually funded the majority of the French fleet, as well as regularly raising tens of thousands of soldiers for the Kings of France.
How different were the Welshmen from Englishmen?
I don't actually know the answer to how aware the French were of the differences between the Welsh and English components of the English armies, but I can provide some clarity on the differences between the English and Welsh. Welsh soldiers usually made up an unusually high proportion of the English armies - I've never seen anyone explicitly say why, but I could take a guess that it was because of a similar reason that Normans were such a large part of French forces - because it was held as a royal demesne for the heir. There was also a rather big difference between the Welsh and English soldiers - Welsh soldiers mostly only spoke Welsh and were the only soldiers to wear a distinct uniform - the red and green livery of the Prince of Wales. However, for the purposes of the rest of the answer any reference to English soldiers should be taken to also include Welsh ones, as the distinction is often not made in sources.
How 'English' were the English armies?
To put it simply, this completely depended on the army. Overall though, the answer would be not very. Very roughly, the English armies can be broken up into five distinct categories: the army in Flanders from 1337 - 1341, the army in Northern France from 1346 - 1347, the armies in Brittany post 1341, the armies in Aquitaine and the mercenaries that spread across France, especially after Poitiers.
To answer this, it's also important to quickly explain how English armies were made. Early in the war they were conscripted, with a subsidy (wage) having to be paid to them if they campaigned outside England, but this took a long time, and results were often disappointing. As time went on, Edward III moved towards a system of retinues, whereby English lords would keep a core of men-at-arms and archers that Edward could call upon in times of war. This meant that these soldiers were more disciplined, experienced and able to fight to together, but also did mean that less men were able to be raised than had been through conscription.
During the spectacularly unsuccessful campaign in Flanders, Edward's army included around 4,500 Englishmen, and at its peak had perhaps 12,000 soldiers in total, the rest of whom were mostly German. This kind of proportion was generally the case for the majority of campaigns across the war, but as I will explain, there were some significant exceptions.
During the Crecy Campaign, Edward III landed an army in Normandy of around 12,000 men. This army fluctuated from between 5,000 and to more than 30,000 over the course of the Siege of Calais, but one thing was constant - they were all English. This army was anomalous not only in being the largest English army ever deployed outside the British Isles until almost 300 years later, but also in its composition. There was no other English army in France that was made of almost exclusively of English soldiers until Agincourt almost 70 years later.
The closest that would come to such an 'English' army would be the armies in Brittany. These were often very small - the peak was around 5000 English soldiers under the command of Edward III in 1343 along with likely the same number of Bretons, but generally it was only around 2000 at most, with Bretons making up around half of the armies.
Armies in Aquitaine however, were almost exclusively Gascon unless England had specifically sent an English army there, something which they often promised to do, but rarely delivered upon. Generally Gascon armies were composed of a core of roughly 500 men from the Constable's garrison in Bordeaux, most of whom were English, and as many Gascon men as could be mustered from whichever lords were loyal at the time.
When England did send reinforcements, the levels of English and Gascon men were roughly equal, for example the Black Prince's army for the Poitiers campaign had around 3000 English soldiers, out of 10,000 total. For the Earl of Stafford's army in 1352, the only army for which we have almost complete records for, there were 3600 Gascon men and 3800 English.
Lastly, and perhaps most importantly, were the bands of mercenaries that spread across France. These were referred to as both English and Gascon, but their composition was completely mixed. Initially they were composed of men from Anglo-Gascon armies who had decided not to return home after the end of a campaign, instead taking a local castle and demanding tribute from the surrounding villages.
There are two important things to note though regarding these bands. Firstly is that it was extremely common for their leaders, especially if they were English, to marry French widows, gaining their lands and their titles in the process. Secondly is that after the battle of Poitiers, in 1356, these spread like wildfire. Many of their recorded leaders were French, but not Gascon, had not fought for the English, and not always even soldiers, but despite this, such men were still referred to as Gascons. Both of these show the blurring of identity across this period, and how fluid labels such as Gascon or English could be - Gascon essentially came to refer to anyone who allied with the English.
How 'English' were the French soldiers in the armies considered to be?
This leads into the last part - how English were these soldiers considered to be. I'm not sure I can answer this fully to the standard of this sub, so unfortunately I'm going to have to leave this element to someone better qualified than me. This is also perhaps the most interesting part of your question, so I genuinely am sorry that I'm not able to answer, it, but I'm looking forward to seeing if anyone else can.
Edit: u/Asinus_Docet has a great answer on the idea of nationality in the HYW, which may be closer to the answer you were hoping for.