We all know the claim was somewhat doused after the hundred-years war, but was the claim to the throne ever really obtainable?
After successfully conquering Normandy in 1417 and advancing further into France, the English king, Henry V, forced the French king Charles VI to negotiate. The resulting Treaty of Troyes ensured that Charles' daughter Catherine would marry Henry and their children would inherit the French crown upon Charles' death. In the meantime, Henry would be regent.
Henry and Charles both died in 1422. Henry and Catherine's son, Henry VI, was crowned King of France in 1431 in Paris. However Charles VI's son Charles VII (who had been crowned King of France in a rival ceremony in Rheims in 1429) continued French resistance to English rule and by the end of his reign in 1461 had reconquered most of France. Had Henry V lived, he may well of completed his conquest of France.
In 1956 during the Suez Crisis, the French premier Guy Mollet suggested to the British Prime Minister that France merge with Britain, with France in the Commonwealth and Queen Elizabeth as head of the French state.