I think that Franz Joseph is the man on the throne, watching Elisabeth being crowned by Gyula Andrassy.
Deffinitively the man on the throne is Franz Joseph, he's wearing a hussar uniform the day of the coronation. According to some other portraits and even one photo, FJ was wearing a (red) hussar uniform at that day. The man in white standing near Sissi looks like FJ but deffinitively isn't he, I don't know who is really he, IMO he's an important noble man as the others near he.
And was this coronation or wedding ? FJ was already Emperor by the time of the wedding Would it have been the practice for the Empress to have a separate cornation after her wedding ?
I don't think that this illustration is of the time of their wedding but at the time of their coronation as king and queen of Hungary. Interesting fact anyways, I always wondered if she would have been crowned too, I haven't read nothing about this, but it's possible.
A pair more of the same event...
The Emperor being crowned, the Empress is at the far left of the illustration
Both together, now King and Queen