The Germans may have "converted" an old merchant marine ship into a light aircraft carrier back then. I can't really remember. Probably flew old bi-planes if so, anyway (bi-planes can take off, and land, in very, very short distances - which is important for tiny/light carriers).
Pretty difficult to project force without aircraft carriers, though. The Germans *badly* lagged in this department, in code breaking, in computers, and in nuclear research.
Of course if Hitler's "Plan Z" had been completed, they would have had a balanced fleet by 1944/45.
As for Aircraft:
Hitler ordered Göring to produce aircraft for the carrier and under this pressure, the air marshall offered redesigned versions of the Junkers Ju 87B and the Messerschmitt Bf 109E-3, which were at that time being phased out of the Luftwaffe first-line squadrons. Raeder was unhappy, but he had to accept them or none at all (including Göring's insistence that the flying personnel would remain under Luftwaffe command). All this forced another delay in the construction of the carrier: the flight deck installations had to be changed.
From here :
http://en.wikipedia.org/wiki/German_aircraft_carrier_Graf_Zeppelin