Germany does not need a large aircraft carrier, a small carrier built on the hull of a Dithmarschen-Klasse tanker will suffice. Relatively small ship with 26-28 aircraft. One training vessel built in 1935 and another in 1936/1937. In OTL, the Kriegsmarine wanted its aircraft carriers to be the eyes of the fleet, they needed to find their targets in some way. Remove Raeder from command of the Kriegsmarine and the navy has a different commander, it is realistic that Germany has two small aircraft carriers before September 1939. One for training and one for combat. The Raeder/Göring hatred in OTL prevented any cooperation. If the Kriegsmarine is headed by someone more politically flexible, some cooperation between the Luftwaffe and the Kriegsmarine is possible.
Combat operations with an aircraft carrier are not doomed to failure, quite the opposite. If the fleet has eyes that seek targets, it is possible that some raids in the OTL that suffered from a lack of support from the Luftwaffe may end up more successful. At the beginning of the war, it is Unternehmen "Nordmark", a sortie by the battleships Gneisenau and Scharnhorst, the heavy cruiser Admiral Hipper and two destroyers into the sea area between Shetland and Norway from 18 to 20 February 1940. Marschall had no support from the Luftwaffe, he could rely on only to their seaplanes and xB-dienst radio operators.
If he was accompanied by an aircraft carrier, locating targets would be much easier. I don't know what kind of aircraft such a ship would have available, maybe the Heinkel company would dominate here as
@Nell_Lucifer wrote. Armament 12 He 112 and 12 He-118...?
An even better chance to succeed is Unternehmen Juno, the original orders for the entire operation were a political order. Raeder felt that the Kriegsmarine had to do something to help Dietl and his soldiers. The original plan for the operation was suicide, as the fleet was required to sail directly into Harstad/Narvik and sink the Allied ships there. Marschall understood that this was madness and defied the order. Instead, he decided to hunt down Allied ships fleeing Norway. When he set sail, he had no idea that an Allied evacuation was taking place. He understood this only later, thanks to his seaplanes he discovered several allied ships, but that was not enough. Intelligence on board the flagship - xB-dienst, revealed the call signs of many British ships, including two aircraft carriers, but not their exact location. Now with the aircraft carrier, his Kampfgruppe has a good chance of locating targets before his escort runs out of fuel and is forced to comply with Hitler's order to withdraw to Trondheim. Almost three hours elapsed between the sinking of the first victim, the tanker Oilpioneer (5,666 grt)/(05:55) and the sinking of the transporter Orama (19,840 GRT)/(08:40). By 13:00 then Marschall could not find the targets and was forced to send his escort away to Trondheim.
It wasn't until 16:45 that the twins found the aircraft carrier HMS Glorious and her escort...
Marschall followed his instincts throughout the operation, not knowing exactly where the British fleet was. If he had more reconnaissance aircraft he could have used the time between 09:00-13:00 and found HMS Glorious or HMS Devonshire much earlier which was about 80 miles from the carrier. There were many more targets in the area, including two large evacuation convoys. Marschall knew they were there because the xB-dienst had picked up their call signs and radio communications. However, he did not know the exact location, thanks to the aircraft carrier there would be a good chance of finding any of these targets before 13:00. Moreover, it is very likely that if he had located at least one convoy, he would have refused to comply with Hitler's order and not send Rear Admiral Hubert Schmundt to Trondheim.
The British were unaware that the German fleet was at sea for the duration of Unternehmen Juno. They only found out when HMS Vanoc and HMS Veteran fished out survivors from HMS Glorious.