One do wonder what kind of bride he could've marry.
Many of his Bonaparte cousins struggled to make royal matches so they married either each other or like in the case of Napoleon III and Mathilde married members of the aristocracy.
Another descendant of the Napoleonic nobility, the future Oscar I of Sweden-Norway was shunned by the royal courts and had to settle for a Leuchtenberg.
The Leuchtenberg themselves must be said to have made the best marriages of all the Napoleonic families with one sister marrying the aforementioned King of Sweden-Norway, one sister the Emperor of Brazil, one the Prince of Hohenzollern-Heichingen, one the Duke of Urach while the brothers married the Queen of Portugal (and his sister's stepdaughter) and the daughter of Emperor Nicholas I of Russia.
My guess is that Franz wouldn't had been allowed to marry a royal but would've been given a bride from one of the more prominent Austro-Hungarian houses.