I went to Narvik last year, studying the battle, and allied operations in the area. A very interesting event in the war, surely, and something of a tragic one.
At this stage in the war, it was clear Norway was going to be lost. So far up Norway's mountainous spine, however, Narvik may have made something of a fortress: Unreachable by rail except from Sweden (with the line that goes through the strategic mines) hard to reach by road (for which purpose the Germans brought in tens of thousands of Russian PoWs to blast tunnels and create enough roads to suit their needs. With enough AA, Narvik may hold out for a good length of time. The ore shipments will be invaluable, shipping supplies to the Soviet Union will be greatly simplified, and the town will serve as a rallying point for the Norwegians who OTL went into Milorg, or to Britain.
On the other hand, keeping the port open from prowling Nazi subs will be expensive to a Royal Navy and a Royal Norwegian Navy already stretched by the battle of the Atlantic. There's also a good chance that the Germans will be able to ship another assault force through Sweden and outflank Narvik through Tromsø, if they don't end up getting Sweden completely on their side as a result.
Narvik will soon become a British and Polish show: even if the French forces stay instead of going home to defend their country, they'll likely be ordered to cease operations by the Vichy government. If Narvik holds out long enough for the Americans to enter the war, it's likely to last out: The Americans could use it to get the battle experience they so dearly needed. They might even be able to make it into the Second front, as Churchill was keen on the idea OTL.