Having enjoyed the English version some years ago, I thought it might be interesting to tackle the German one.  On inspection of the publication details at the front of the book, I noted the following:

Alle Rechte vorbehalten

Copyright © 1985 by

Diogenes Verlag AG Zürich

500/86/8/9

ISBN 3 257 01678 6

It struck me that being German, Süskind must have originally written the book in his mother tongue and a quick Google search confirmed this.

According to Daniel Kampa, An author “contacted Keel to ask if he would read the manuscript of his novel. The author was Patrick Süskind and the novel was Perfume. Keel planned a first edition of 50,000 copies; Süskind suggested 5,000. Neither man could have been more off track. Since 1985, the novel has sold 12,5 million copies worldwide and has been translated into 38 languages. It was the turning point for Diogenes, the publishing house founded by Keel in 1952“. 

So the true first edition of “Das Parfum” was in fact a German language version published by Diogenes in 1985 and English language versions entitled “Perfume: The Story of a Murderer” appeared shortly afterwards in the UK and the US.  Since then, the book has been translated into at least 46 languages (goodreads currently lists 218 different versions).

Incidentally, I’ve no idea whether my copy is a true first or not, even though the ISBN 3 257 01678 6 matches editions claimed in bookfinder to be firsts.  Perhaps the code 500/86/8/9 is a clue?