In the 9th district, there is a curious little island of French culture. This stems primarily from the presence of a French high school/gymnasium back-to-back with a former French cultural palace. Due to this quirk, the tram lines between Schottentor and Währingerstrasse/Volksoper are often buzzing with French conversation. It would be a crime, therefore, to not supplement this without at least one decent French restaurant.
While many visitors may not want to embrace French culture while in Austria, Café Francais (just north west of Schottentor) is a nice way to soak it in without making it too obvious. The waiters only partially speak French and the cuisine is not 100% authentic. But the café is definitely chic, the coffee is strong, and the moules frites are perhaps the best in the city.
The place gets really packed during the school year and at high seasons and French becomes so prevalent that you will double-check your GPS. But not to worry, Café Francais will not let you forget where you are, serving solid seasonal dishes that favor the Austrian specialities such as white asparagus. You will then be able to have the best of both worlds and feel only marginal regret as you choose the moules frites over a schnitzel (as I know you want to!)