Because Edward III claimed to be the legitimate king of France through his mother Isabella of France. Isabella was the daughter of the French king Philip IV and married Edward II the king of England. She had three brothers who were in the line of succession when Philip IV dies. However after Philip IV's death all three of her brothers died in quick succession as well, leaving her the lone serving child of Philip.

Therefore if one were to believe that succession can run through the female line, then Isabella's son Edward III (from whom all subsequent British monarchs are descendant from) were the legitimate king of France as well as that of England. However the French crowned Philip IV's nephew Philip VI instead, as under Salic law inheritance does not run through the female line. Edward III chose to press his claim and this was largely what the Hundreds year war was fought over.

Despite losing the Hundreds year war in the end, the English monarchs maintained their claim to be the rightful rulers of France until the French revolution when they dropped that claim as part of a peace treaty with the French Republic.

King Philip IV the (Un)Fair of France and I of Navarre, husband of Queen Jean I (reigned 1274-1305), the heiress of Navarre, died in 1316 and was succeeded by his son Louis IX and I (reigned 1314-1316) and by Louis's posthumous son Jean I (1316-1316), then by Louis's brother Philip V of France and II of Navarre (1316-1322) who died without sons, followed by their brother Charles IV of France and I of Navarre (1322-1328), who died without sons.

The French nobles decided not to give the throne to any daughter of Louis X, Philip V, or Charles IV, in part because their wives, a daughter of the Duke of Burgundy and two daughters of the Count of Burgundy, had been involved in an adultery scandal and the nobles could not be certain that the alleged daughters of the former kings were actually their daughters.

So for this and other reasons (but probably not the Salic Law that wasn't cited until decades later) they gave the throne of Navarre to Joan II, hopefully the daughter of Louis X and I, and gave the throne of France to Count Philip of Valois, the first cousin in the male line of Louis X, Philip V, and Charles IV. Despite the the claim of King Edward III of England to the French throne as the son of Isabella "the she wolf of France", daughter of Philip IV)

Actually the real female line heirs of France were Queen Joan II of Navarre (1328-1349), daughter of King Louis X of France and Navarre (1314-1316), and her son King Charles II "the Bad" of Navarre (1349-1387).

But since Navarre was small compared to England they couldn't do much fighting to claim the French throne.

Edward III and his successors for generations fought to conquer all France and kept the tile of King of France even after losing the 100 Years war. That was nothing unusual. There were many other examples in medieval and modern times of two or more monarchs claiming the title of king of the same kingdom. For example in World War I the Central Powers included the Kingdom of Bulgaria and Austria Hungary whose monarch's titles included King of Bulgaria and the Allies included the Russian Tsar who also claimed Bulgaria among his titles. The title of King of Jerusalem was claimed by the rulers of Austria, Italy, and Spain as well as as several heirs to defunct thrones.