'Appointment' is "aftale" which also means agreement or deal. "En time" means 'an hour' or if you are in school 'one class session' however long that actually is.
"A hour" is not correct. It is "An hour". People in England tend to drop their "H's", i.e. "Otel" instead of "Hotel", and therefor "A hotel" becomes "An otel". If you want to play it safe, always say "an" before words beginning with a vowel, and "a" before words beginning with a consonant. However, there are very few exceptions, "an hour" being one of them.
Some people use a instead of an when the word beginning with h has a consonant sound at the start "an historic" but that would not apply to "an hour". I'm not sold on this I always use an before h- words but then again I pronounce the letter with a vowel sound "aitch" instead of "haitch".
What about "he has a time on Saturday" for something a receptionist would say in reference to an appointment?
That would be "han har en tid på lørdag" not "en time" which means 'an hour'.