Not fighting for it did not mean refusing to take part in the contest. Even if they had no interest, they could still join the fun.
With Austria's current strength, no one could afford to ignore it. Austria would not be denied its due share.
Even if it did not compete for colonies, it could still obtain compensation. Concessions made here could be offset by gains elsewhere.
The exchange of interests was the essence of international diplomacy. How could one possibly expect to take all the advantages without paying any price?
If all the benefits went to one family, how were the other countries supposed to get by? If they could not provoke you, could they not avoid you? They could simply refuse to play with you.
This was not yet an age in which one power stood alone. No country could cover the sky with one hand. If one did not want to become utterly isolated, it was best to follow the rules of the game.
Once the rules of the game were broken, the greatest losses would inevitably fall upon the rule-makers. The rules themselves had been established by their makers to safeguard their own interests; once the cards were reshuffled, no one could guarantee that they would still hold the leading position.
As it happened, the Anglo-French-Austrian Triple Alliance were all old imperial powers. They had personally participated in and dominated the formulation of those rules, and the current rules themselves represented Austria's interests.
With the broad policy settled, Franz no longer needed to worry about the specific negotiations. What they could obtain would only become clear after the talks were over.
Franz could not possibly judge every country's strategic objectives. Any talk of making targeted preparations in advance was complete nonsense.
It was like British diplomacy.