Weirdly I actually think 1945 is not only the latest you're getting but probably the best bet for an Anglo-French union that lasts until today.
While it's true most of the above examples could unify the English and the French under a single crown the locals have a completely different cultural and linguistic heritage unless you manage to butterfly away nationalism such a royal union seems like if it's not already destroyed through succession crises (the English crown are sufficiently separate it's an easy way to divvy up land between two sons), you'd instead see a probably English uprising (more geographically concentrated and increasingly demographically a lesser party) with the rise of nationalism leading to independence.
So I'm not convinced there is a POD that would lead to a union that will last till the modern day unless you go so far back that English and French stopped having much meaning.
But if you go much later a political union becomes much more possible as international cooperation becomes more of a norm (plus of course it's closer to today so easier to have at last into the modern world as there is less distance to travel)
Having said that it's true the 1945 proposal was not a true and lasting political union but it could easily be the first step to one, it feels more like a way to have a French government in exile fully integrated into the British war effort in a way that saves French blushes about the loss of the mainland, with an expectation that it's not going to last much past the war.
However deploying a flight of butterflies we could probably see that morph into a permanent political union I'd say something like this
The union plan goes ahead letting the British effectively inherit to the French Navy and more quickly occupy the French colonies the Germans still managed to take mainland France (and effectively force a local level capitulation) so you have a separate and even less legitimate Vichy government, and an Anglo-French government.
Possibly due to the British being more assertive due to inheriting more military assets from the French, there able to scare Japan off and you either see a more limited conflict in the Pacific or (ideally) no war with Japan, this in turn butterflies away Pearl Harbor and delays American entry into World War II, the Germans invaded the Soviets more or less on schedule American aid is flowing, but they can't manage to get enough commitment to have the US fully and formally join with the US instead playing the world's banker on very friendly terms. However American guns and gold are enough to help the Soviets turn the tide and by the time the Americans do join (if at all) the Iron Curtain has fallen a lot further west, with Anglo-French forces managing to liberate France Belgium the Netherlands etc but at least Germany and everything East about firmly in the Soviet sphere.
So you have a very active and immediate Soviet threat to the East, a lot of goodwill between British and French elites with the surviving French elites being those who are willing to make a deal with the British, and a less directly involved US. At this point I could see the Anglo-French union continuing (probably the French effectively being integrated into a Commonwealth with teeth) as at least an interim to help counter the Soviet threat.
Then just keep having events happen that continues to push them together, e.g. a Suez equivalent where the US manages to put its foot in it even more in relations between the British and the French making them feel they can't trust the Americansm a middling European power (maybe Italy) collapsing into a nasty civil war because of Soviet influence; making ever increasing political union be seen as a necessity to protect the interests of both countries abroad.
By the time you get to the 80s or 90s I could see a working political, economic and military union with a common currency a federal Parliament and government (granted probably with a lot of devolved powers to the individual member states), possibly directly integrating a few smaller and easier to hold bits of both of their empires, and as part of a wider Commonwealth of both former parts of empire and some surrounding countries e.g. Belgium and the Netherlands which might look a bit more like the EU which is reasonably politically stable and likely to exist more or less indefinitely.
