Continuity of the Crown
Many people wonder or question the practice of the French pretenders using regnal numbers when they aren’t actually on the throne.
This is because of one of the Fundamental Laws called Continuity of the Crown. It says that once the king is dead, the next in line is automatically king. France, therefore, can never be sede vacante, for France always has a king.
This began when Philip III dated his reign from the date of his father’s death rather than the date of his coronation.
This was strengthened by Charles VI, who declared that his successor would be king immediately following his death.
After the Revolution
The practice continued after the Revolution. When Louis XVI was murdered, royalists instantly recognised the Dauphin Louis-Charles as Louis XVII of France.
And once the little king’s unfortunate death was confirmed, royalists recognised Louis Stanislas Xavier, Count of Provence as Louis XVIII.
This continued with the recognition of Henri, Count of Chambord as Henri V.
Henri V died in 1883. Thus began the current dynastic dispute between the French House of Bourbon-Orleans and the Spanish Bourbons.
Most royalists, even Legitimists (much to the dismay of Anjouists today), supported the Orleans, recognising the Count of Paris as Philip VII of France. The Legitimist supporters of Philip VII became known as Fusionistes or Unionists, in English.
Since then, Unionists (true Legitimists) and Anjouists have used and recognised regnal numbers for their pretenders.
The tradition continues today. That is why those of us on the monarchical right recognise Jean IV, Comte de Paris as King of France.