The "rightful heir" to those crowns is whoever, if anyone, the legislatures say is the "rightful heir".
So there is no "rightful heir" to the crowns/lordships of Ireland and France (except to the extent that Northern Ireland is unified with Britain) because those crowns no longer exist, and as for England, technically that crown no longer exists, having been unified with the crown of Scotland by the Acts of Union 1707 to create the crown of the United Kingdom of Great Britain (later Great Britain and Ireland, later Great Britain and Northern Ireland, and then also the crowns of the Commonwealth realms, which has varied through the years but currently sits at 16, including the United Kingdom), and succession to that crown is determined by the Act of Settlement 1701 and Succession to the Crown Act 2013 (repealing the Royal Marriages Act 1772).
The only thing left, really, is to change the succession of British peerages to absolute primogeniture.