un calendrier is a noun, calendaire is an adjective.

Calendrier is a name: Un calendrier, le calendrier.

Calendaire is a qualifying adjective (it is an adjective that does not belong to the current language, it is a word of the legal or administrative language)

Wordreference doesn't even list "calendaire" as a word in French (http://www.wordreference.com/fren/calendaire ) So unless it's a recent addition to the French language, I regret to inform you that your classmates who use "calendaire" are wrong. :/

Edit: However, Wikipedia does have an article on "Calendar Day." (https://fr.wikipedia.org/wiki/Jour_calendaire ) I'm not sure if the spelling of "calendar" is specific for the holiday or not. Also it's Wikipedia, where anyone can write anything, so take this as you will. ;)

http://www.larousse.fr/dictionnaires/francais/calendaire/12307?q=calendaire#12153

I use calendrier and thats what shows up in google