From the LIFE magazine archives.
Joe A. advised in an e-mail of 19 May 2012, "Your legend identifies it as being taken just before their assassination in 1914, but this isn't correct. There are several details that show it as being taken at a different point in time:
1) The Archduke is wearing a kepi and overcoat. On 28th June 1914, he was wearing a cavalry general's dress uniform with a cocked hat decorated with green plumes.
2) The Duchess is wearing a fur coat, which places the time of the picture as being in winter or early spring.
3) The couple is sitting in a horsedrawn carriage, not an automobile.
4) If you look at the far left of the picture, you can see the brim of the hat of a woman sitting opposite Franz Ferdinand and Sophie. That is in fact their daughter and oldest child, Princess Sophie.