@Ionus,
Philip III Capet, in the direct or "right line" of descent from Hugh Capet, died late in the 13th century, at about the time (perhaps a little later) that Edward succeeded Henry III, who was the son of John, which provides the link to the Robin Hood story (and so far as anyone can prove, it was just a story).
Philip had two sons, one of whom became his successor, Philip IV, and the other was Charles de Valois. That Philip, Philip IV, had four children who survived into adulthood, Louis, Philip and Charles, all of whom succeeded him on the throne, and Isabella, who had been married off to the Prince of Wales, son of Edward, and to succeed in his own right as Edward II. Philip's first cousin, Charles de Valois, had a son, Philip, who survived into adulthood.
When Philip IV died, he was succeeded by his son Louis,
who had no adult son. When Louis died, he was succeeded by his brother Philip, and when he died he was succeeded by his brother Charles. In two cases, there were surviving daughters, but no surviving sons. So, when Charles died, the French invoked an alleged Salic law that no woman could succeed to the estate, and therefore, the throne passed to the son of Charles de Valois, who became Philip VI.
The Salic laws were not alleged, but no one has ever provided reliable documentary evidence that the Salic laws prohibit inheritance or rightful descent in a distaff line. This was true in the 14th century, too, apparently, because Edward III--son of Edward II and his wife, Isabella, daughter of old King Philip IV--rejected the claim about the Salic law, and claimed that he was the most direct descendant of Hugh Capet, and therefore was the best candidate for the French throne because of descent "in the right line."
I believe, however, that Edward made his claim prior to 1340--the naval battle of Sluys was in 1340, and i think Edward declared his intention to take the French throne in 1336. That's a trivial consideration, of course. What was significant was the use of the longbow
en masse. The French King employed Genoese crossbowmen, and Beauvais archers who also used longbows, but the French chivalry despised them, and charged through them on more than one occasion, squandering the advantage they might have provided.
The Robin Hood story relied upon claims about using the longbow. Many amateur "historians" will point out that English yoemen were required to practice "at the butts" every Sunday morning, and that football and other sports were prohibited for that reason. Those claims, however, ignore the relationships in time. Walter Scott's version of Robin Hood places him in the reign of Richard, 1189-1199. Modern writers place him, on documentary evidence, in the early 13th century, if indeed he ever actually existed.
But the longbow was not known in England then, and Edward's requirement for practicing at the butts dates from, obviously, after his succession to the throne in 1272. The Angl9-Saxon warriors did not use the longbow, certainly, and although Saxon peasants my have hunted with bows, the longbow was not introduced into England until Edward subdued the Welsh. Llewellyn the Great has supported Simon de Monfort, brother-in-law of Henry III, in his rebellion. Llewellyn had brought to the battles he fought the longbowmen of Powys in South Wales, having overawed and secured the allegiance of the Lords of Powys and of South Wales.
But Llewellyn's principality fell apart after his death, and he was "succeeded" by his grandson, Llewellyn ap Griffith, who could not secure the allegiance of Powys. When Llewellyn ap Griffith himself fought against Henry and Edward, the longbowmen of South Wales remained aloof. When Henry died in 1272, and Edward came back to England, his first serious public measure was to attack Llewellyn with the intention of subduing Wales. (Henry had thought to make Edward the Prince of Wales, but Llewellyn the Great had had other plans. Edward eventually made his son Edward the first non-Welsh Prince of Wales.) This time, the men of Powys came in on the side of Edward. It was after the successful conquest of Wales that Edward required English yoemen to practice at the butts with the longbow.
In his campaign to subdue Scotland, Edward was confronted with the use of the shiltron by the Scotts. A shiltron was roughly speaking the equivalent of a shield wall, and was usually a circular formation, intended to fend off heavy cavalry. The Scots typically, though, did not use shields, they used bucklers, and you can't make a shield wall with that. So they used long sharpened stakes which they planted in the ground to hold off heavy cavalry.
Edward incorporated both the long bow, and "shiltrons" of bowmen behind sharpened stakes. His poor, pathetic son Edward II made no use of any of his father's military techniques, but his grandson Edward III did. I suspect that Edward only intended to use his claim to the French throne in an attempt to regain at least part of the formerly claimed Plantagenet lands in France. The Garonne remained loyal, more or less, which no doubt arose from the fact that the English were the best customers for Bordeaux wines. But Poitu, Anjou, Normandy and Brittany were no longer even notionally English. Edward began his active land campaign against the French with an invasion of Normandy. At Crécy, in 1346, the French chivalry charged the English, first cutting down the Genoese crossbowmen in their path, and over a distance of several miles, and involving them in a swamp. Philip had tried to prevent them, but they wouldn't be gainsaid. They exhausted their horse in attack on the Genoese, the long approach ride, and getting through the swamp. Even though the English position was on a low slope, they were worn out by the time they got there. Behind their sharpened stakes rammed in the earth, the longbowmen slaughtered the French in an appalling manner.
I think then that it dawned on Edward that he might really make a war of it, and to his profit and that of England. The war was not popular, but as long as he was winning, he could carry it over the objections of the people, and of a weak Parliament. (His grandfather, the first Edward, had created the permanent Parliament, taking a page from Simon de Monfort, who had called a Parliament during his rebellion against Edward's father Henry III.) Thereafter, Edward's son, Edward, Prince of Wales, known as the Black Prince, carried on the war in France. A decade after Crécy, the son of Philip VI, Jean le bon, proved that the French had learned nothing. They had the English surrounded near Poitiers, and could have bagged them by simply sitting down to wait. But the French chivalry wanted "glory," and Jean was foolish in a way his father had not been. He not only allowed the army to attack, he lead the attack. By some bizarre line of reasoning, the French decided that they had lost a decade earlier because they had been mounted, so this time they attacked on foot! Not only were a great many of them slaughtered this time as well, but Jean and his son the Dauphin were both captured.
The heyday of the longbow was long after any plausible allegation for the lifetime of Robin Hood. The Robin Hood stories are entertaining, but bear exactly that relationship to history that Christian Science does to science.