So, some food for thought. The Franco-Prussian War was one of the biggest game-changers in European history and would help set the stage for future European and global effects. Furthermore, we know the story on how the war started and how Bismarck helped manipulate the events with Napoleon III being strung along?
What if Napoleon III wasn't in power?
What if in, say in between 1863 and 1865, the Second French Empire fell and the Third French Republic was born. I won't give too many details since it could steer focus away from the point of the thread (which tends to happen alot.) But I will say that the French incident in Mexico was alot worse and led to France losing pretty much all its holdings in the Americas.
So, it's 1965, the French had gotten rid of their monarchy that gotten them in a war they lost and alienated the US and Mexico. How would they deal with Prussia? I doubt they'd want to go to war given the loss.
What would Prussia do with little chance in goading France?