Academic years in my culture are specified using two-year format e.g. academic year 2014-2015 (which starts in September 2014 and ends in June 2015). The term "academic" bears, in my opinion, much of an academic context. Are there any alternative options to be used when referring to such a year in a primary or secondary education context?
"School year" is also OK.
But "academic year" is fine, even for elementary schools.
Maybe "school year" can be used so that there is no objection even from those who think school has mainly some purpose other than academics.
By the way, I don't think "academic" will suggest "academy" to most people.