English, like German of today, used to use "to be" as the auxilliary of intransitive verbs (ones that don't have objects, e.g. to fall, to go, to stand...) and "to have" for transitive ones (ones that have objects, e.g. to see, to hit, to take). Nothing more mysterious: if you go through the KJ you'll notice the usage.
Yes, that's exactly the case. French as well uses être instead of avoir to conjugate the past tenses of a specified list of intransitive verbs.
I do notice, however, in English as I understand and use it, a slight difference between "Christ is ascended" and "Christ has ascended". The former shifts the emphasis to the present reality, whereas the latter emphasizes a bit more the verbal aspect. Neither one is really wrong, and in fact, it would be difficult to express that nuance in French, for example.