War comes to Norway later in 1940 or possibly 1941 at the latest. It is plausible that Germany would decide to concentrate on France first. In this case, the British would mine Norwegian waters. After the fall of France, both Britain and Germany would have strategic needs to take Norway. Germany would end up taking Norway due to being stronger on land and air. Butterflies:
1) If the British shut down iron ore from Narvik in 1940/1941 winter, it will slow German production.
2) Britain may move first in the ATL. The British also likely attack the French fleet in Oran in OTL. The British will look more like the aggressive war party compared to OTL, so it will be harder for FDR to come to Britain aid. If the major USA military registration bill is changed or FDR is not able to provide lend/lease support to the UK, there are major changes.
3) The invasion of Russia is likely impacted. After the fall of France, there will be an additional war in Norway. The British may do the Norway operation instead of operations related to Greece.
4) Germany actively fighting in Norway may delay the Central European countries allying with Germany, since Germany victory will be slower and less decisive than OTL.
In summary, Germany will still end up with Denmark and Norway, but the operation could take months is the British land forces get there first, and especially, if the RN does a max effort to defend Norway. Narvik is conquerable using over land forces only, but the terrain is hard to operate over. In the ATL, the British probably destroy the port in Narvik and much of the railroad leading to Narvik from Sweden. This harms German arms production substantially. To outsiders such as Americans, the moral difference between the British and the Nazi's will seem smaller. The invasion of Russia will be changed, but it is hard to quantify how it will be changed. A war in Norway after France is a major strategic change, and will have many ripples in time.