Short answers, pulled from the story.
The Hundred Years' War began in 1337 following a succession crisis after Charles IV of France died without sons or brothers. Edward III of England claimed the throne based on his mother Isabella being Charles's sister, but French nobility rejected this claim to install Philip VI instead.
The English won the Battle of Crécy in 1346 through the effective use of longbowmen which caused a complete disaster for the French army. King David II of Scotland was defeated and captured at the Battle of Neville's Cross on the 17th of October 1346 while attempting to invade northern England.
Between 1347 and 1351 the Black Death ravaged Europe with 6 to 12 million people dying in France representing 30% to 60% of the population. This demographic collapse resulted in major labor shortages and economic collapse that hampered the ability of both nations to fight.
Joan of Arc entered the city of Orléans on April 29 after persuading the Dauphin to send her to the siege in April 1429. She raised troop morale to attack English redoubts forcing them to lift the siege and allowing French cavalry to break through near Patay losing 2,200 men.
The closing battle of the war was the Battle of Castillon on the 17th of July 1453 which marked the first major battle won through extensive use of field artillery. The French camp laid out by Jean Bureau opened fire causing severe casualties including the death of Talbot and his son while ending England's continental possessions except Calais until 1558.