How? Battle of france is over. Germany would be delighted to have a front where it has all the supply advantages and its numerical superiority can be readily exploited. The estimate was that the allies would need something on the order of 250000 troops to have a credible hold on the region. Germany would have air superiority and a largely free hand to move supplies up the coast and supplying the allies would risk ships the RN simply could not spare at the time.
With the battle of France it's a sideshow. Without it it becomes a major focus point where a relatively quick German victory can be seized with relatively modest means.
Germans may end up losing significantly less air assets if the allies decide to stay as a continued war in norway would be a far less risky affair compared to BoB.
For the OP conditions to work, the German timeline has to be slowed down by greater losses during the invasion - pick your poison: more ships sunk or damaged, the airborne forces aren't as successful, earlier Norse mobilization (which would also bring the Norwegian 6th Division to Narvik earlier). As it was, the French and Norwegians drove the Germans mountain troops out of Narvik about at the start of the Battle of France. Historically, pretty much everything broke the Germans way. Any upset to the timetable and Narvik likely is retaken earlier, which allows for a defensible line somewhere between Narvik and Bodo.
As you note, once the Battle for France is over, Norway is a sideshow - for the Germans as well.... Their focus would be on Britain. Historically, they waited till mid September to call off the invasion plans - not the best time to start a campaign in northern Norway. The Kriegsmarine is shot up, the airborne forces have also taken damage (Norway, and Holland/Belgium). They may re-group and try again to finish the job in the spring of 1941, but then other strategic goals come into play.