I assume that there would be some sort of Free France or France government in exile (at least in Moscow

) sooner or later. My interpretation of the thread is, that there is no "De Gaulle-FF" directly in June 1940, contesting Vichy for control of the French colonies.
At the very latest, summer 1944 would see a pro-Allied French Government, but the probable date for that would be after the liberation of Algiers in the course of Operation Torch.
A major long-range impact might be an entirely different attitude toward France by the victorious allies.
An even worse one?
Internally, the French could still create enough myths about a nation completely being part of the Resistance.
Well, at least France fought in 1939 and 1940. So to say.

And then it was occupied/neutral. Or one could say it was a compliant semi-ally of the Axis in OTL already.
French would fight again 1944 onwards- even Italians fought against Germany at that point.
For who were the Free French? A useful fraction of renegades, handily with some troops willing to fight, but with a leader who was a pain in the...
They were at times seen as useful by the other Allies, but often enough as an utter nuisance.
Concerning the UN, how about a comparison with Denmark? Denmark didn't have a government in exile either, resisted for two hours in 1940 and yet it was a founding member of the United Nations in 1945. But you are right, I see the Security Council seat for France gone (which might much later on pave the way for a European seat).
Of course, the situation would be wholly different if France joined the Axis as a belligerent power. But that would be a different thread.
I cannot see the French empire being dissolved akin to the Italian colonial possessions. I am sure that Britain wouldn't allow that to happen as this would put an immense pressure upon it to immediately let go of its colonies as well.
I still assume that France would become a nuclear power in the medium run, as long as it wouldn't be explicitly forbidden to do so (which I do not see). Also, a weaker France might even more so try to strengthen its influence through European unification. Also, there is much more to European unification than a mean to control (West-)Germany, though this idea came back to the surface at the time of re-unification. It was even more a mean to strengthen the Western European economies, raise the level of national income and thus to fight Communism- and also to prevent any new wars among the European nations.
the major powers might suspiciously see this as a dangerous potential consolidation West German power in Europe - a sort of "lose the war, win the peace" thing for Germany.
Happened anyways.

Ask Maggie.