I've just done a search, and it seems that the defeat of Germany's invasion of Norway in 1940 has not been truly covered--touched on, alluded to, yes.
In that search, a number of suggestions popped up as to how the German invasion might fail. If Norwegian fortifications are alerted properly, German ships may have a much riskier time landing troops through the southern fjords. Give the populated parts of Norway a bit more warning and time to mobilize, and German airborne forces in particular will face a lot more trouble securing airfields. The Royal Navy also had a couple of opportunities to blast the German surface fleet that it missed out on as well.
There must be a number of other things that could break for the Norwegians or the Allies, or against the Germans, but leave that aside for now.
What does the rest of the war look like with the Allies victorious and entrenched in Norway? Presumably, the Kreigsmarine has been gutted, and German airborne divisions suffering severe attrition. The Royal Navy probably suffered a bit in those engagements as well, and perhaps learned a few lessons on the little matter of ships vs aircraft. None of this is enough to stop France from falling, and victory in Norway might actually come after Paris sues for peace.
Once France does fall, what can Germany do to defeat Britain? Failure in Norway won't improve enthusiasm for any sort of cross-channel invasion, especially if the German surface fleet is mostly underwater. It's been covered numerous times about how incapable the Luftwaffe would be at covering an invasion or forcing the UK to make peace as well, and Allied airbases in Norway could help keep attention on German u-boat production.
Do we see a "Battle of Britain" across the North Sea in general, in an attempt to isolate and weaken the Allied position in Scandinavia? What do the British do with their Norwegian options after the Fall of France?
Germany is going to suffer in the longer term with seasonal difficulties in iron ore shipments, even putting aside British efforts to interdict that trade over the Baltic. Sweden herself is in an extremely awkward, precarious position now. Does this situation result in Swedish loss (or abandonment) of neutrality?
Just what kind of war are we looking at after a German defeat in Norway?