Franz was also very interested in opening up colonies. However, his view differed from others; it wasn't simply about plundering wealth from overseas.
The Habsburg dynasty had existed for too long; an ancient empire signified conservatism and rigidity. Even though the rebellion had led to a reshuffling, the path to ascent remained narrow.
As a member benefiting from the status quo, Franz certainly couldn't choose to start over. Therefore, the only solution was to enlarge the cake. With a bigger plate, naturally, more opportunities would arise.
Expanding in Europe was too difficult, and even if successful, it would not be without consequences. Overseas colonization, on the other hand, was different. With Austria's strength, getting a piece of the pie was no issue at all.