Hi Michael, a pertinent question.
Before Louis invaded England, a whole load of shenanigans went on behind the scenes — mainly in France- to lay the groundwork for invalidating John as England's rightful ruler: John had been condemned in the English court for treason against his brother (although Richard forgave him), condemned in French courts for murdering his nephew, he had been excommunicated for a time, his Barons no longer supported him and had invited Louis in and so on.
Louis was also clever enough to pursue the claim under his own birthright, rather than embroil his father in it, as his father had signed a truce with John previously.
Whether these claims would have been enough to permanently gain Louis the throne was never tested because John died and the game changed.
As to the anointing, unfortunately for Louis - although possession might be 9/10ths of the law and he had the might and potentially the right - the Archbishop of Canterbury, Stephen Langton, (no fan of John himself) was abroad at the time and no other bishop was available to carry out a full coronation ceremony with an official anointing in Westminster. Louis was not King of England ‘By Grace of God’.
If John had lived and/or been captured by Louis the situation would have been very different and perhaps the case made for declaring John an illegitimate King, rendering his own coronation and anointment invalid, but that is, of course, a matter for speculation.
It’s a murky matter for sure.