My take on the French Core mood is that it is mixed. Some great triumphs, but also an awareness that something is very wrong.
As I run it, the French retain the classical view that the nation represents civilization. They are, and have been for as long as anybody remembers, THE superpower responsible for everything. Yes, others have contributed in valuable ways, but the French empire is the spearhead of mankind, the leader of the free world. Think of current America (including its hurt surprise when ungrateful foreigners criticise its good intentions) - including that a sizeable number of the citizens are getting pretty tired of the current government.
The French empire is getting into serious instability. The years under emperor Ruffin may have been politically stable and relativly free compared to under the junta, but the economic prospects don't look great, French pride has been hurt and domestic problems are building up - massive corruption in some parts of imperial france, high taxes to finance the vast spacefleet, criticisms over the handling of everything from the Kafer war and colonial independence to agricultural subsidies, Saharan transports and the relationship with the arabian neighbours (given the composition of the empire, it is safe to say that France and the arabian nations have close and complex ties). It might just be too high expectations, but it could also be the kind of decay that marks the end of a colonial empire.
One key problem might be that as the central power is struggling with slowing growth and enormous expenses the rest of imperial France suddenly feels left out. Why spend those megalivres on the French Arm when the Senegalese peanut farmers cannot afford to upgrade their hydroponics? When will the trans-Saharan railway be online again - it is *much* more important for more people than terraforming Sans Souci. As long as everybody saw that the future was brighter than the present they would accept whatever Paris said. But if the money is not coming, the economy is not growing and the bureaucracy is stifling - local elites are getting restless and disloyal.
To me, as an extremely non-nationalistic Swede the most alien part of the setting is the nationalism. I think it is essential for understanding how the empire holds together: it is the force that may make the French try for a new government or a new policy, rather than dropping the empire. To quote one of the rebel NPCs in my campaign:
"France is something far more than the current Empire. The third Empire will pass just like ones of Napoleon I and III, a temporary ripple on the sea that is France. France is a civilization: a culture, a way of life, a set of ideals, an identity. It is represented by the tricolore, be the meanings of its colours "Paris and the rest of France", "liberté, égalité, fraternité" or "loyalty, purity and bravery".
We might rebel against France on Earth. We might set up our own just government and perhaps remain a nation apart for all time. But that does not mean we are leaving French civilization. We are the Kimanjano part of this civilization."
As an aside, I think racism is an interesting angle of the French empire. On one hand the different people have been together for a long while in a successful empire with mass communications. On the other hand there is still a clear distinction between metropolitan france and the periphery, and pretty clear centralistic views of what constitutes proper culture. I would expect racism among the French to be less about skin color and more about integration: can you speak proper French and refer to the "in" media stars, or are you a colonial bumpkin? (I always thought the picture of the emperor in 2nd ed looked rather african, in fact)