"The first sentence is basically correct"

Apart from the number of years that had passed since the execution of Joan of Arc there is not one single thing that is accurate in the sentence quoted:

"Today, May 30, 2015, is the 584th anniversary of the day on which Joan of Arc was burned at the stake by the British forces occupying France."

1: 584 years back from 2015 gives the date as 1431, simple arithmetic, which would tell anyone who knew anything about the history of the British Isles that 276 years would have to pass before any "British" forces could possibly set foot on French territory.

2: Anyone who knew anything about what was called "The Hundred Years War" would know it as a series of conflicts waged from 1337 to 1453 by the House of Plantagenet, rulers of the Kingdom of England, against the House of Valois, rulers of the Kingdom of France, over the succession of the French throne. At the time English Kings descendants of William the Conqueror held in their own right by inheritance and through marriage vast tracts of land in France, land that was subject to predation by the Kings of France, there was no British occupation of France