I polled several dictionaries and style guides on the proper use of "apropos" (/A-pro-POH/), which I've only ever seen in phrases like "apropos of nothing" (= "this isn't related to the current topic, but …"), and the general "apropos of x" (= "since we've been discussing it"; as in "apropos of breakfast, I like eggs").
"Apropos" is from the French à propos, "to the point" or "to the purpose," and it can be used with or without a preposition as an adjective or an adverb. It describes something or an action as timely or appropriate. "Apropos" can also be used as a preposition, with or without "of" or "to," and means "with respect to" or "regarding" (Webster's Third cites "'apropos the return of young Americans to lyricism'" and "'his remark to Emerson apropos of diplomas'").
When using the preposition, English-speakers generally use "apropos of." Additionally, there are a number of 20th-century citations with "apropos" and no appended preposition; but there are many fewer citations for "apropos to." (See Merriam-Webster's Dictionary of English Usage.) "Apropos of" sounds most correct to me, and Henry Fowler and Merriam-Webster seem to prefer "apropos of." Fowler favors "apropos of" on (in part) the shaky grounds that it translates a cliché that must once have been well known: à propos de bottes (bottes = boots). À propos de bottes was used to switch to an entirely new subject.
"Malapropos" is available to English-speakers too. It's probably only an adjective or adverb, meaning "inappropriate, inopportune," and takes no appended preposition.