For reasons I can't explain (maybe someone more accomplished in English grammar
can) accomplished is wrong in your sentence and must be substituted with 'attained' or 'achieved' or 'reached'. But one could think of examples where language *could* accomplish something:

"The English language has accomplished what no other language has been able to accomplish - the attainment of a global status"
"The only thing that English has accomplished is the destruction of regional dialects"
"The regulatory language has accomplished its objectives"

Agree - it's "achieved," "attained," or "reached." And I also can't explain why!

A difficult question, I'm confused too - but let me try: 'accomplish' describes something you did successfully and may look at with pride and satisfaction.
There's something more to it, I know, but I'll be damned if I can focus it properly.

> "The English language has accomplished a global status"

To accomplish is to reach some sort of goal, or finish a task. "A global status" is not a goal. That is what's wrong with the usage. One could however say "The english language has accomplished the goal of having a global status." That is correct, AFAIK.