Without claiming any expertise, in fact without denying gross ignorance, I would suppose that some Japanese at some time called Mt. Fuji "Fujiyama".

I doubt that this pronunciation originated through a misreading of the kanji by a foreigner. Most foreigners can speak at least a little Japanese before confidently reading Japanese kanji, surely. The exception might be somebody familiar with Chinese, who would offhand read the "yama" character as "san"/"shan" or close enough. Anyway, one would ask his local friend what that big mountain over there was called, I suppose.

It surely looks as though the name "Fuji no yama" was used in Japanese long ago: for example, here is an old transcription in Latin: