I figure it depends on how the Soviets play the situation. Say we put the turning point of the war at Moscow in 1941 (instead of Stalingrad or arguably Kursk in '42/'43) and the Red Army pursues the Nazis across Eastern Europe like IOTL, things could get a bit...hairy for the rest of the continent. The Soviets were hellbent on destroying the fascist Axis, and without the western Allied powers opening a second front with Overlord/D-Day or Operation Husky (Italy), they'd have no reason to stop their campaign in central Germany. You might very well see the Red Army rolling up to the English Channel, or swinging south to bring the fight against fascist Italy. Or both. And then there's the question of Spain, which I'm not particularly knowledgeable on to be honest, but given the prominent role of Communists in the Civil War, it's entirely possible Franco would be on the hit list too.
Once the war is over? I doubt the Soviets would have the desire or manpower to occupy most of Europe (Japan will still be a thorn in their side)...but Soviet-backed Communist governments would probably spring up all over the continent, given what happened IOTL shortly before and after WWII. Greece and Italy had sizable Communist movements of their own who likely become dominant in this scenario. If Franco gets it, Spain probably goes that way as well. Don't know enough about the politics of the rest (France/Belgium/Denmark/Netherlands) to really speculate on their paths. Things would then of course get very tense with the UK and US, neither of whom were exactly fond of socialist-communist ideology or Stalin's expansionism. I'm doubtful that either would actually to directly attack Soviet Europe, but it'd make a very interesting Cold War situation.
And of course there's the Pacific Theatre as well, which I honestly don't know enough about in terms of Soviet involvement to comment on, but as a wild guess, things go very badly for Japan and probably Nationalist China too.