I have studied and now teach French, but I'm unfamiliar with both this author and his book. Since you've asked about its date of publication rather than about its content or style, I thought I'd try to find an answer for you.
I couldn't find much about the author. When I searched for Madame Olympe, I got lots of hits for Harry Potter, but few about Murger's novel. I was able to find it on books.google.com, which has a couple of different versions. The first one I checked must be the edition you have because it is dated 1860 as well. I continued to search on books.google.com and found an edition published by Michel Levy freres in 1854. I also found a "new" edition published by Levy in 1866. I couldn't find any other editions of the book. So it seems that the first edition was published in 1854 and that you have a later printing of the same edition.
Some interesting trivia: The author's name is Henri Murger, but he anglicized the spelling of Henry to make himself seem more "elegant and noticeable."