There can't be a PoD before the 1st September 1939. Nazi Germany must be, in geopolitical terms, 'crushed' to count as an Allied win. At no point does either the United States or Germany/Italy declare war on each other. The US can fight Japan. The Soviet Union may join the Allies, as OTL.
Big swooping invasions and operations asides, how would the combatant nations and their peoples be affected? I would suppose that the Axis would have a slightly easier time and the Allies would have to make up for an awful lot of material advantage, and fight for a period beyond 1945. What sort of repercussions would that entail? Also, how about the post-war world, what would the Balance of Power be?
For added difficulty, have the PoD after the 22nd June 1940, when France signs the armistice. It is totally fine for French colonies to either immediately or eventually come over to the Allied cause.
The most obvious thing is for France not to fall in June 1940
Perhaps a larger more effective Battle of Arras - Frankforce is not repulsed and the 3rd Light Mechanised Division (3rd DLM) manages to launch its assault into the flank of a German effort to dislodge Frankforce on the 23rd May
50th 'TT' Div + an entire Tank Brigade attacks and additional French Units
Rommel is badly wounded and his adj killed attempting to rally element of his Infantry that had broken in the early stages of the battle and an Armoured car Squadron overruns a heavy flak battery in column of march before terrorising rear echelon units for the next few hours
A fanatical counter attack by elements of the SS Totenkopf Division later in the day almost stops the British attack but despite its fanatism its inexperiance (relative to Heer units) leads to heavy casaulties (particularly among Junior officers and NCOs) early in the battle and by night fall the Divisions fighting arms are shattered - in some cases completely routed.
Panic ensues as OKW beleives that 5 british Divisions (4 of which the German Intellegence services were unaware of) have attacked and that both the 7th Pz and Totenkopf divisions have been destroyed (Mauled and partially routed but not destroyed).
A Halt order is given to the 'Sickle cut spearheads' as the German high command feeds more forces into that particular fight.
The
Leibstandarte SS Adolf Hitler attacks positions held by the now understrength 8th Battalion Durham Light Infantry who had dug in over night.
Both the 8th DLI and the 2 fighting battalions of the LSSAH are shattered and the SS unit's fantical assaults are no substitute to its lack of infantry experiance and training which result's in very heavy losses particularly among its Junior officers and NCOs.
While this attack 'goes in' the German high command now convinced that the panzer army is going to be surrounded by some cunning British Plan using divisions that were hidden from them order the spearhead to prepare to break out back along the way it attacked and attempt a smaller encirclement to the one planned.
.....and so on
Basically Case Yellow fails to deliver and the Battle for France devolves into a battle of Attrition after the failure of the Panzer Army to encircle and destroy the BEF and Mobile forces in Belgium and North Eastern France.
The Line is stabilised and the French High command is given breathing room to reinforce, reorg and get a grip
As the weeks pass the German attack runs out of steam and while the Entente are pushed back almost as far as Paris - the Heer and LW are both exhausted particularly among the Elite pz and LW ground attack formations and Material losses are heavy on both sides.
1940 closes with a 1914 Xmas type opposing trench lines (in reality a very long skirmish line with defence in depth and large reserves).
By June 1941 the BEF in France is now 20 Divisions Strong + 3 Indian and 2 Canadian Divisions, with the French adding 5 more
Franco British Airpower now out numbers the LW by more than 2 : 1 and a newly establish chain home line and additional airfields allow the airforces to establish air superiority
In north Africa Wavel Leads a victory march into Tripoli after O'conners Victory earlier in the year in Cyrenaica and French forces besieging Tripoli after heavy fighting on the Tunisian Border
The Entente War council had maanged to convince Churchill to reinforce success and no troops are sent to reinforce the Greeks (who as it turns out were quite capable of handling the Italian invasion on their own) or were any of O'Conners troops sent to East Africa before it was Clear that the Italian forces in North Africa were finished.
and so on...