How is King Lear complicated by English-French relations?

Shakespeare treats the French landing on English soil gingerly. His English theater audience will not like this incursion, regardless of the fact that the French are only there to restore King Lear to his throne and are, in effect, allies rather than invaders. At the very beginning of Act IV, Scene iii, the Gentleman establishes that the King of France is not even present.The Gentleman tells Kent in vague terms that the French king had to attend to
Something he left imperfect in the state, which since his coming forth is thought of; which imports to the kingdom so much fear and danger, that his personal return was most required and necessary.
But the real reason for excluding him was that his presence would make the intrusion look more like an invasion. With the French king gone, it is Cordelia, an English girl and daughter of King Lear, who is at least the spiritual leader of the expeditionary force. She is a sort of English Joan of Arc. Shakespeare has downplayed the French invasion ever since Gloucester first hinted at it to his son Edmund in Act III, Scene iii. Shakespeare realized that treating the matter as the French coming to the rescue would seem unpatriotic and not only offend his audience but might get him in trouble in higher places. At the same time, Shakespeare realized that Lear's only chance of obtaining revenge on his hated daughters and their husbands was in being restored to his throne; and that would require military assistance from a foreign power. Rather ironically, it was because he disowned Cordelia that she married the King of France, and her husband is only sending his forces to England because he loves Cordelia and Cordelia loves her father.
Although it would seem that the French invasion was intended to be a rescue mission, the French had to lose the battle for patriotic reasons. In the end both Cordelia and Lear are prisoners and the English are totally victorious. The rescue is a complete failure. Cordelia and Lear both die. It is the conflicts among Goneril, Regan, Albany, Edgar, and Edmund that restore order. Dover is mainly significant because it draws all these characters, as well as Lear and Kent, to the one spot where the French are landing. But the French have to be defeated, and Lear has to die, since this is his tragedy.
https://www.owleyes.org/text/king-lear/read/act-iv-scene-i