I would have considered a carrier in the North Sea very useful for Operation Sea Lion, the invasion of Britain. You could play some hide and seek there with the british navy while storming the english southern shores.
Edit//: That is what I always did in HoI2. I jumped with 8 paratrooper divisions into southern england and placed my Kriegsmarine fleet with 1 carrier in the mouth of the Thames. This attracted the complete british fleet and soon i was fighting several carrier fleets. As soon as my carrier was inoperable I withdrew. Enough time for a landing at Edingburgh with 4 armoured divisions, 2 mobile divisions and 3 mountaintroopers. Mountaintroopers take Scotland and rush for Scapa Flow while the tanks and mobile Divisions hit the brits in the rear and fight their way to the paratroopers isolated in the southeast. Only the 9 cargo ships got lost.