With the conclusion of the Prusso-Russian War, Frederick's marriage was also put on the agenda, a significant event for Austria.
Hanover had long failed to gain control over the German Federation Empire, and the Duchy of Baden had played a great role in this. Without them leading a group of small states to oppose the Central Government in the Imperial Parliament, the German Federation Empire wouldn't have been so severely fragmented.
Of course, Austria had also exerted significant effort. Without the support of the Vienna Government, the Grand Duchy of Baden wouldn't have been able to pull together so many allies.
This marriage alliance was actually Franz's way of encouraging the Grand Duchy of Baden not to be timid and to continue opposing Hanover, assuring them that Austria would have their back should trouble arise.