Learn English – Is it acceptable to use “is become” instead of “has become”

The use of "is become" here relates to verbs of motion/transition; verbs of motion would take be while other verbs would take have. There is no such grammatical distinction in English perfect forms anymore.

English began with this distinction, as did sibling languages like German (as Cindi pointed out originally in a now-deleted answer).

Here is what happened after that. This is an excerpt from the OED's discussion of auxiliary have:

In early ME., [have extended its use to the verb to be, as in "have been", like French]. Verbs of motion and position long retained the earlier use of the auxiliary be; and "he is gone" is still used to express resulting state, while "he has gone" expresses action.

This is talking about English retaining the auxiliary be for motion verbs, like present-day German. Originally, the verb "to be" also used be as an auxiliary for the perfect, e.g. "it is been cold", but changed to have in early Middle English. (German still uses "ist gewesen", or "is been", today.) After this change, the other motion verbs still retained the be-auxiliary for perfect.

In Modern English, the motion distinction completely faded out, and be was replaced with have across the board, except in a very specific case. The OED describes this case:

in intr. vbs., forming perfect tenses, in which use it is now largely displaced by have after the pattern of transitive verbs: be being retained only with come, go, rise, set, fall, arrive, depart, grow, and the like, when we express the condition or state now attained, rather than the action of reaching it, as ‘the sun is set,’ ‘our guests are gone,’ ‘Babylon is fallen,’ ‘the children are all grown up.’

Keep in mind that become is not intransitive, so "is become" doesn't work anymore, with any meaning, in present-day English (— except, of course, in poetic use).