If Norway is an Allied success but Hitler still invades France, I could see Barbarossa being either postponed or cancelled.
USSR would still invade Finland, but you'd have British and French troops going from Norway to support Finland.
If a Dieppe style raid took place on Germany in say 41 then I could see Hitler being deposed by the Army shortly afterwards. Bombing raids are one thing, but for the English to set foot on German soil is another thing entirely in the Prussian mind.
Then it gets sticky. If a de-nazified Germany then sues for peace with Britain and France, would Soviet Russia feel betrayed, and Given Stalin's five year Military plan would have seen the USSR at what he considered full strength by 1942, would the Soviets tried to invade western europe? (Britain, France, Germany and the USA(?) against the Soviet Union)?
Alternatively, there's nothing to stop the USSR going to the aid of their Communist bretheren in China and making war on Japan.
That would leave the British especially, and the French in an odd position - fighting each other in Finland, fighting a common enemy in the far east.