The Norwegian campaign was a long one, the second longest the Germans fought, and went on for six months. It only ended with the Fall of France, among constant counter attacks by the Germans forcing the Allies from Narvik. What if however the Allies never leave Norway, instead reinforcing their toehold through June and into July; possibly even expanding it some. This would force the Germans to divert forces to keep them bottled up in Northern Norway. Would that have a major effect on the rest of the War in Europe?
your whole premise (or at least your arithmetic

) is
incorrect ...
the OTL Norway campaign started with the German sneak attack on 9 April 1940
and ended with a formal surrender on 10 June .. though the Norwegians had ceased fighting a couple of days before
2 months not
6 ,,, 62 days
With a few exceptions the immediate Norwegian response was ineffective
and in practice all Norway's major cities were captured (or surrendered) to the Nazis within hours or days.
Given Norwegian losses on equipment, especially air power, in those first days
only British Naval strength and the British and French soldiers and air squadrons ferried across the North Sea
permitted any effective resistance beyond that point.
Despite that effort the whole of Central and Southern and central Norway had to be abandoned by the Allies by 5 May i.e
before any action in France.
Once that started on May 10, no further Allied reinforcement could be countenanced.
The french collapse was clear by May 22 and therefore planning for a possible complete evacuation of Norway began on May 24th
(There had already been several small scale lifts of troops cut off by German successes)
The Norwegian King quit the country on 7 June
while the last British and French troops were gone by the next day, covered by those few Norwegian forces still able to fight.
The French surrender on June 22 was the final nail in the coffin for Norway.
With the equipment losses at Dunkirk and an immediate air threat Britain simply could not help further.