As a question word, "when?" (= at what time?) can be followed by the future tense. Consider this answer to your Q: "I will see you when (=at the time that) you call me." The first clause - the main clause - is again in the future. But the when-clause is not a question. It is a subordinate clause in a complex sentence that refers to the future. In such clauses, we normally use a present tense in the when-clause. We do the same with some other conjunctions e.g. before, until, as soon as.

I think the opposite that Jeff does, but it might also depend on the context. To me "when do I see you again?" implies that you both expect to see each other regularly (for example, if you regularly see your doctor once a month, or you have a weekly lesson with a tutor, etc.). It might be a little rude if the other person doesn't share that same expectation. "When will I see you again?" is probably more general and works in any context.

Besides the grammatical considerations, there is also the following nuance... When do I see you again? --- it implies that there is no certainty in the future that you two would meet up. When will I see you again -- there is certainty in the future that you two would meet up