In other words, how far into the war did governments/the press start to recognize the war as some kind of sequel or 'recurrence' of the original Great War? Was the concept first mentioned in English?
OED says that the Manchester Guardian coined "World War No. 2" on 18 February 1919, "with reference to an imagined future war arising out of the social upheaval consequent upon the First World War (1914-18)."
Their next citation for "World War II" is Time Magazine on 11 September 1939.
The phrase "Second World War" appeared in Political Science Quarterly in September 1942; but it had been previously used by H G Wells in The Autocracy of Mr Parham in 1930.
Similarly, when did the term "World War I" first appear?