France is not going to war with Germany without Britain. The two must stand together.
If the West does not go to war, then Hitler wins yet another high risk gamble. Germany and the Soviet Union basically partitioned Eastern Europe through the M-R Pact. Stalin is probably disappointed that Germany is not at war with Britain and France, but he has a very good deal with Hitler. Will Stalin go to war against Finland and move against the Baltics? Hard question. Certainly Stalin would like to do so, but with Britain and France not at war with Germany, such a move carries a risk that the West may decide on war to help defend Finland. Stalin was usually reluctant to make such blatant moves alone. He liked to do so when other great powers were distracted (with Germany and West at war), or in collusion with them (the agreement with Germany or his gains at the end of WWII with compliance of the West). It all depends on how adventurous Stalin is. I personally think Stalin will attempt to win some sort of advantage, but not risk a situation where war would happen. Instead, he would hope to place himself well for a future time when the West and Germany would be at war.
Hitler and Mussolini planned for a general war by 1942. After 1943, the West would be sufficiently rearmed to not give a relative advantage to Germany. But 1939 was considered too soon. So likely World War II will start in either 1941-1942. In any case, the longer the delay the more advantage it is to the Allies.
I expect Hitler still intends to settle matters with Britain and France first - the ones he thinks are of a greater threat than the Soviet Union. I don't see him attacking Stalin first.
An invasion of France one or two years after it did IOTL will turn out differently. British and France will both have far better defences they did in May 1940. France will have brand new frontline fighters, Britain will have lots of Spitfires and radar all over the place. Likewise they'll have better tanks, although their doctrine will still be inferior. But without the exact circumstances of the "sickle cut" through the Ardennes (still always possible), it's hard to say how things will turn out. However, given time the West might have enough time to learn from the German experience in Poland. Probably not enough time for real reforms to be made
With the conquest of Poland, it's possible that Belgium (or even both Belgium and Netherlands) will attempt an integrated defense of Western Europe. It's very hard to say how the politics will turn out if anti-appeasers win a general election in Britain (which must be done by November 1940 at latest). A no confidence motion may even bring down Chamberlain earlier. No one in Europe will follow Britain as long as Chamberlain remains in power. And any new leader will need to be bold to fashion an anti-Hitler front in the West (Eastern Europe will already have have adopted pro-Germany positions).
In any case, Churchill is unlikely to be the new PM as the Conservatives won't win the election. Labor will form the new government. Churchill might be given a cabinet position if a wartime coalition forms.