A good starting point is the Soviets taking Italy and all of Germany.
They don't really need to take it all; as the Germans have aptly demonstrated in WW2, you can somewhat easily drive across West Germany straight in to France. West Germany by itself is no defence; that's the whole reason West Germany got admitted to NATO and allowed to remilitarise - everyone knew that they needed West German soldiers to provide some level of roadblock, to allow them time to be able to fire a nuclear missile and therefore render mutual destruction as a plausible deterrent.
In this kind of TL, I can't see NATO being a thing, as a Franco-British unified military will be able to justify it's own defence without leaning on the Americans - and for national pride reasons, they won't want to lean on the USA. If they do, they admit the union between them is kinda pointless; the point of the union is to provide effective and efficient defence (amongst other things).
De Gaulle was a fiercely patriotic person, this was the guy who made France a nuclear state and swapped France's US dollar holdings for gold (he viewed the dollar reserve currency system as America's exorbitant privilege, it cost just a few cents to print a $100 bill but foreigners had to provide $100 worth of goods and services to obtain one). I think he'd work to break it off this union once Paris was liberated.
Didn't he also vote against letting Great Britain into the EU? Twice I believe...
Probably not as IIRC he was only appointed as a junior minister during the middle of the fall of France in 1940. Assuming that the Union went through with Reynaud and Lebrun continuing to maintain their positions, or equivalent ones, with a France that fights on it doesn't leave a vacuum for de Gaulle to move into. He might be able to move up to more senior position like Minister of War and National Defence which would help boost his profile and reputation but nothing like our timeline.
Firstly, de Gaulle barred the UK from entry to the EEC twice - but this was predominately as the UK was viewed (and still is) as the little puppet of the US. CDG feared the UK joining the EEC was a step to allowing stealth control of Europe by the USA. If France-Britain (et al) are a union, then this fear isn't a thing - the UK is quite clearly and demonstratably the closest ally of France, whilst being a friend of the USA too.
Plus, as Simon says, de Gaulle only got to where he was post war by being the leader of the Free French. The whole notion of Churchill's UK-FR union was that legally France and the UK merged; ergo there is no France surrender, and therefore no Free French. CDG would probably end up in Government, maybe in Cabinet as a Defence Minister or something, but he's not going to be anywhere near as powerful as OTL.
IIRC when Britain applied to join the EEC the first time around Denmark, Norway, and Ireland also applied to due to their strong economic ties to the UK. If Britain is a founder member it likely also brings them in as well I'd expect.
Denmark and Norway I can't quite decide about. Churchill's Union was explicitly about military and foreign relations, and then economic. Can the Franco British Union (even with the 4 I've posited) guarantee the defence of Norway and Denmark? To be honest, I don't think so. Also, any visibly lasting Franco-British Union I can see spurring a United Scandinavia, with that state taking on armed neutrality, but closely linked economically with the UK-FR Union.
