Translation:Is this the first time you learn Vietnamese?
Yes, it would. I would naturally ask this question as "Is this your first time learning Vietnamese?" However, I suppose because "your first time" is a possessive phrasing and there is no such possessive phrasing in the Vietnamese, perhaps "Is this the first time you're learning Vietnamese?" would better reflect the syntax of the Vietnamese.
In either case, "Is this the first time you learn Vietnamese?" is not how to ask this question in English. Since "to learn" something is a process, we use the continuous/progressive tense not the simple tense. The Vietnamese may use the simple present here, but the English does not. "Is this the first time you're learning Vietnamese?" (Reported 2019-09-03.)
There doesn't seem to be anything grammatically wrong with "Is this the first time you study Vietnamese?" but the tense refers to habitual or customary behavior and strikes the native speaker as a bit strange because "the first time" would seem to be a one time thing.
Native usage seems to be more nuanced with regard to tense. "Is this the first time you have tasted pho?" or "Is this the first time you will have (are having) pho?" both seem more natural but both depend on conceptual placement of "the first time" somewhere on a linear time line before or after the positing of the question. In other words, the speaker conceives of "the first time" as past, present or future and forms the tense accordingly.
Since a language course is a lengthy thing by nature, how the speaker deals with the relationship of " the first time" and the tense is flexible but she or he is very likely to treat it as a solitary, not on-going or customary, event.
If this is a question, when the speaker speaks, his/her voice will begin low and then raise at the end of the question (stress at "tiếng Việt"). If the speaker speaks at slow speed, his/her voice will stress at two places: "lần đầu tiên" and "tiếng Việt".
And when this is just a statement, the speaker's voice is normal, not up, not down.
Since both words refer to the acquisition of knowledge, they're semantically close, but they aren't full synonyms.
Specifically, study is but one way to learn:
You can learn by studying. You also learn through experience. Or, you can learn through instruction.
The opposite direction doesn't work... You can't study by learning. You can't study by experience. You can't study by instruction.
In other words, "learn" refers to acquiring knowledge. "Study" refers to one particular way in which to learn. Study is a subordinate to learning in a categorical hierarchy
Bad grammar in English: "Is this the first time you HAVE TRIED TO learn Vietnamese?" or the "first time you HAVE STUDIED Vietnamese?" When I first took Vietnamese (50 years ago) I learned that "hoc" means "to STUDY" in English. This sentence is a good illustration of why. In English, "study" is something one does; "learn" is what happens to one when the studying is successful.