Edward III was the grandson of Edward I, the infamous Longshanks of history (think English King in Braveheart), and he really lived up to grand-dads legacy. Over his 33 years of rule he fought an unbelievable number of battles, captured and held prisoner two kings, and at the end of it got France to sign over 1/3 of their kingdom. But this was the beginning, now he was fighting the French King Philip VI about which one of them should be the king of France. Edward, obviously, was based in England. Philip was in France. Edwards problem was to demonstrate how he was the rightful ruler of France, and how to convince the population of that as well. His options were limited to really just two: Outright conquest (not viable because France was much bigger and Edward really could not sustain an army overseas for that long), or successfully embarrassing Philip to the degree that both the people of France, as well as chunks of the nobility, would see Philip as so weak and ineffective that they would come over to Edward on their own. Enter the Chevauchee.
Chevauchee, which can mean either a simple horse processional (ie a casual ride with your buddies), or cavalry charge if taken literally, actually refers to a larger idea: A massed raid, moving through enemy country and burning/looting/smashing as broad a swathe of land as possible. For a modern American example see the American Civil War and Shermans March to the Sea, but much more brutal.
Normally this sort of thing was done to collect loot, and capitalize upon an enemys weakness or lack of speed. But Edward had a second issue in mind, he wanted to fight, not just run. According to historian Rogers, the chevauchee in this case was a deliberate lure to bring Philip and his nobles to a pitched battle.* Even though Edward knew well that meant fighting outnumbered he had a deliberate reason for this. The justification, again, was to demonstrate Philips weakness. Not only could he (Philip) not protect his people from the depredations of Edwards army, but even when he caught up to the English if he was defeated despite having much greater numbers the confidence Edward was trying to undermine could likely crumble.
By the measure of the other battles I have talked about thus far (Cannae and Verdun) you might not think the numbers involved in this battle are very impressive. None of the contemporary accounts match each other and modern historians generally believe the French numbers were exaggerated, for a variety of reasons. So the total number of combatants here was probably in the range of 40-50,000 troops total.
Edward, it is estimated, probably initially landed in the second week of July 1346 with around 15,000 men. Broken down this was probably around 2,700 men-at-arms (knights, esquires and their like), 2,300 light spearmen from Wales, and maybe as many as 7,000 of Edwards secret weapon the longbowmen from both Wales and England. (See some video explanations here and here, but if you really want to geek out ) The rest was a combination of light cavalry, mounted archers (with short-bows) and other troops. But that is not how many he had at the time of the battle a month-and-a-half and several hundred miles later. By that point he had already fought a couple of small battles, and having captured many prisoners along the way, sent them back to England under guard for later ransom. So at the time of the actual Battle of Crecy it is likely that he was down to around 10,000 men.
A brief word about those longbowmen. The weapon was one that first came into play when Edwards grandfather finally crushed the Welsh people as an independent entity and wrapped them into what was becoming Britain. Because of the topography of Wales, and to some degree their own sub-culture, the Welsh had always focused on more lightly armed and armored soldiery. Theirs was a way of war that focused on hit-and-run, and when pressed, to pull back into their mountainous central retreats. Central to this centuries-long military evolution by the Welsh (prior to Edward Longshanks finally crushing them at the end of the 1200s) was the use of bows and spears. For them, therefore, bigger bows meant longer range and the ability to beat the more heavily armored English upon occasion. The Welsh longbow became their most feared tool of war. And so when Longshanks finally extracted fealty-through-submission from the Welsh he took the best parts of their abilities, the things that had caused him the most problems, and incorporated them into his own armies. By the time Edward III came to the thrown the technology had spread, and would continue to spread, across more and more of England. But the best of them were, still, the Welsh longbowmen with their 6 long war bows which had a pull weight of 120, 140, or even 170 pounds. That is a serious weapon.
Philip had a wider range of troops, and undoubtedly quite a few more. Although original accounts put the number under French command at as much as 8 times as large as the English, that is mostly discounted now. The best historians seem to be comfortable with a number between 30,000-40,000; the majority of which were mounted knights and mounted men-at-arms. The next largest contingent was actually crossbow-carrying mercenaries from Genoa, of whom there were perhaps as many as 8,000 at the battle.
That morning of 26 August the English army made a deliberate and casual march to the northeast, to Crecy and some high ground directly astride the French Armys route. The French were coming from 14 miles to the south. This ground had been selected earlier by several of Edwards primary subordinates, deliberately to allow the English an anchor both of their flanks on poor terrain and to give them an uphill advantage. The English arrived around mid-morning and set about preparing the battlefield. Among other things they dug thousands of 1 wide holes to their front to trip up the French cavalry. Then they set up with three successive lines of infantry in the middle, and wings consisting of the archers on each flank. Nobody was mounted at this point.
The French, for their part, marched pell-mell from their location as soon as their scouts returned and informed the King Philip that the English were setting up for battle. Yes, we know that Philip was under some serious political pressure at this point. After all, so far Edward had pretty much marched unopposed across a good chunk of the north of France, at one point within mere miles from Paris. Philip was already embarrassed by the fact that he could not even stop Edward at any of the rivers, the Seine and the Somme, which could have stalled the latter and forced a change in the campaign. So politically he had to fight, and he had to fight soon. But there was another aspect to this calculation at the Operational Level of War: Food.
Edward, recently, had captured a large store of food, so he was well set. Given the relative rates of speed of the two armies he could have continued on his merry way to the north, picking any one of a number of harbors from which to be resupplied or to leave. Plus, his army was smaller. Philip, on the other hand had a comparatively massive army (larger than most cities of the day, barring London and Paris), and with that theoretical advantage came a very real pressure: he had a lot of hungry mouths to feed and nothing even remotely resembling a modern military logistics system to provide food and fodder for 30,000 men and probably in excess of 100,000 horses. Nor could he loot the countryside of his own people, as Edward had been doing, for obvious reasons. So fight he would, as soon as possible.
Sources differ again here as to what happened next. Quite a few later historians took the line that the French arrived at the battlefield and immediately rushed into battle without getting set and attacking deliberately. This is almost certainly untrue, as the first forces committed were those Genoese mercenary crossbowmen, and mercenaries dont rush into battle for the love of fighting. They go in deliberately, when ordered to do so by the man paying the bills. Yes, the French nobles were itching for a fight, but Philip at least held them together until the whole army was on-hand. But they did appear to attack rather quickly after their massed arrival, and that things fell apart fairly quickly after that.
In a way it doesnt really matter, because the result was the same. Pitting the Genoese crossbowmen against the English longbowmen was a losing proposition for the former, both because of range and rate of fire. The Genoese were slaughtered, and started retreating. Of course this annoyed the assembled French nobility, who then decided to attack their OWN mercenaries from behind. Nice move that one.
Next came the first of several mounted French cavalry attacks. We know that there were three general assaults (the first of which swept through the Genoese, slaughtering them as they went but also getting disorganized. The second and third waves, following, could not see what was going on up front and crowded forward themselves, increasing the chaos on the French side all the more and creating what the modern military might call a target rich environment for the English longbowmen on the flanks. All of these French attacks came to ruin. None of them seriously broke through even the first line of the English knights and men-at-arms on foot in the center. Where there were some local penetrations reserves from the second line (not even the third) of the English, stepped up and crushed it, even as the longbows continued to pour in the arrows from the sides. In the end it was a complete and utter rout.
Casualties, like the numbers present overall, are somewhat problematic to nail down precisely. In part this is because the chroniclers of the time focused on the nobility and just gave sort of a mild hand-wave at the lesser ranks. So we know that among the French both Philips younger brother, and his nephew, were killed, as was the King of Bohemia (a French ally), as well as another seven counts and viscounts, eight barons, and some 80 bannerets, as well as a full 1,542 knights and esquires. The Genoese, who started with roughly 8,000, were essentially wiped out. We have only estimates for the common French soldiers. Overall you might assign a total loss of perhaps 8-10,000 total killed or captured.
The English lost around 300 men, as best we can tell.