Either usage is possible as well as the use of the auxiliary phrase "going to" or the present continuous:
He will go...(He'll go...)
He is going to go...
He is going
Arguably the simple present and the present continuous speak with more certainty about the arrangements than do the modal (future) or the "going to" constructs. Otherwise, the options are equally valid grammatically and equally idiomatic, perhaps slightly less for the modal usage.
And idiomatic English does not mean the same thing by "the next week" and "next week". "The next week" is idiomatic ONLY in reference to a previously designated (future) time. For example, "Thanksgiving is the 4th Thursday in November. We go on vacation the next week."