In actuality, Sisi's relationship with Franz Joseph wasn't as romantic as in the show. While Franz Joseph was passionately in love with her, Sisi never felt fully the same way and was emotionally distant from him and she ended up avoiding him and court life as much as she could.
Helena frequently refers to Sisi as a peasant. In fact, Sisi was the grand-daughter of the King of Bavaria and her mother Ludovika was actually the sister of Archduchess Sophie of Austria (Empress Sophia in the series). Therefore Sisi was the cousin of Franz and of much higher rank than the Viscountess Helena.
In 1867, Emperor Franz signed the Ausgleich, which officially turned Austria into Austria-Hungary. Both countries would have their own governments, with a shared head of state. Count Gyula Andrassy was the first Prime Minister of Hungary after 1867.
In real life, Sophie (Sophia) was never Empress of Austria. She convinced her husband to abdicate during the Revolutions of 1848. Therefore Prince Franz was in fact Emperor when he first met Sisi.
Sisi's sister Helene, who was likely the inspiration for the character of Helena, did eventually find a husband following rejection by Franz Joseph. She married the Prince of Thrun and Taxis and arguably had the only happy marriage of any of her sisters.