'Adieu' is too common in English (and American) to be considered an indication of origin. Posted in Mudcat are popular songs, cowboy songs, etc., with the word 'adieu.' Look at the Levy Collection,
(Adieu, my native shore (Lord Byron), The Soldier's Adieu (Dibdin), Adieu, My Native land (American), a Civil War song by Hewett, Adieu Sweet Girl (American, about 1800), There is a tavern in the town, Flash Lad, etc. etc. etc.
A look through the Bodleian Collection yields many more- and these are just those with the word in the title.