The Matter at Issue: The Throne of France
The Hundred Years War was fought largely over who would be the king of France. The English kings, who had originally been French nobles that invaded and conquered England in 1066, still held lands in France. The English lands in France had long been viewed uncomfortably by the French king. Through the 13th century, strong French kings had reclaimed French lands held by the English kings. By the early 14th century, three events came together. First, the English kings noted that one more push by the French would deive the English completely out of France. Second, the French were entering a period of weak kings. Third, the English throne was now occupied by the young, vigorous, able and (ultimately) long lived Edward III. In any other circumstances it would appear absurd for the English king to come up with the idea of claiming the French throne in order to protect English lands in France. But Edward III was bold and, in one of those uniquely Medieval ironies, he had law and custom on his side. The English claim to the French throne was strong, as were the English armies and Edward IIIs resolve. The resulting war outlived Edward, and his great grandson, Henry V, came within a hair of actually taking the French throne.
The items below explain the situation in rather more detail.
Historical Kings of France
Historical Kings of England
The English Position of the Throne of France
The French Ultimatum
A Summary of Overlapping Claims to Various Thrones