After being insulted by Bismarck, Napoleon III hardly had a choice of how to react - overwhelming demand of society and parliament forced him to go to war.
British support for greek war of independence was largely a result of widespread sympathies for greek rebels in british society.
XIX century was an era when even small diplomatic failure made people take to the streets.
I suggest that in Vic3 your population should very strongly express their views on how well are you guiding their country to take its rightful place among other world powers.
If they feel insulted, they will be greatly upset if you just let the whole thing go, without proper punishment. If they consider bosphorus vital for your countries interest, they will expect you to prevent Russia from taking it. Obviously the more democratic your country is, the more you have to care for their views.
Your population should support a foreign policy that makes sense - this could be defined by a set of rules:
- cultural proximity: Austrian and Prussian pops won't let other powers touch their German brothers
- religion: Russian pops will greatly support wars in defence of orthodox nations
- strategic interests: pops of every country should sometimes support policies preventing other powers from taking control of very strategic areas, like bosphorus, Suez Canal, Malacca strait, etc.
- ideological support: revolutionary countries should be very strongly inclined to support fellow revolutionaries
- atrocities: generally pops of every great power should support punitive measures against countries committing atrocities against own peoples
- opportunities: population should expect you to take advantage of obvious opportunities: Japanese population should be expecting you to try to seize some far east russian lands during its civil war
To sum up, there should be direct connection between your foreign policies and your pops. They should get extremely angry if you pay with their sons' blood for some land they consider completely irrelevant. They should be happy and supportive if you achieve success in the field they consider important, boosting their national pride.
Game (via your pops) should support consistent foreign policy that makes sense; no to complete randomness. It should make you feel that every step in international politics has way deeper meaning than painting some more map and getting a bit more population.