If, hypothetically, a Third French Empire had been created would the Bonaparte monarch be called Napoleon IV, as the Prince Imperial of the Second Empire never actually reigned, or would he be called Napoleon V, conceding to a completely hypothetical reign of the Prince Imperial after Napoleon III's abdication?
Perhaps it would depend on whether the Third Empire wishes to repudiate the Third Republic by disregarding its legitimacy, or embrace the legacy of the republic as a new "Liberal Empire".
What are your thoughts?