Well hope America starts conquering stuff soon.
Well they have to get their own house in order after the British kicked the door in and ransacked the place. The US economy has fallen into ruin thanks to the war with the government teetering on bankruptcy.
What will be Napoleon II's stance be on press censorship?
Will Napoleon II hire caricature artists to attack his foes?
It's too early to say, but I think it might be similar to what Napoleon III did in otl, though maybe it would be accompanied with some more dynamic action from the Imperial government. So there would probably be state sponsorship of various individuals to run propaganda to counter the narratives asserted by Napoleon's opponents be they Royalists, Republicans, or others. He might take example from his grandfather who was known for operating an effective and elaborate spy network within Austria.
Though it should be noted that Napoleon III's Empire had a later problem of widespread corruption due to this sort of pseudo-state patronage. Though Napoleon III brought back some practices used under Louis XIV where non-nobles could buy aristocratic titles and gain favors in government. While this helped Napoleon III maintain power, it backfired when it came to the French military whose elites became set in their ways resisting Napoleon III's plans to reform the army. Though the Second Empire did field quite a number of innovative weapons during the Franco-Prussian War, and had the French Army been able to reform itself and gain better leadership it probably could have won the war.
France learned its lesson later with General Boulanger whose reforms helped to modernize the army. Though he was quite a destabilizing force in French politics as well as he nearly brought down the Third Republic. Napoleon II has to manage the system with caution within France as well as abroad to avoid losing total control in this age of Revolution and disruption.
What would Napoleon II do to arrest the demographic decline of France?
Well I have some plans in mind immediately he take the throne that would probably address this somewhat.
As for specific policies, it's too early for me to say as while France's population growth rate is concerning, it didn't really become noticeable until mid to late 19th century. Funny thing is that I was reading some research
articles/studies about this topic when I got the notification for your post.
How would the Capetian Dynasty (including the Houses of Valois and Bourbon ) be remembered in this Napoleonic France?
Well its complicated to say the least. Napoleon II in some ways might present himself as maintaining the traditions of France. Though at the same time he would likely have to cast himself as distinct from the Bourbons/Capetians.
I'd say they'd probably be viewed in a similar vein to the Merovingians, or Carolingians who had various periods of ups and downs before their dynasty faded away into irrelevancy. Its quite ironic that the Carolingians got deposed in a similar manner to the Merovingians though unlike the last Merovingian who was forced into a monastery, the last Capetians lived on as the Counts of Vermandois until the early 12th century with Countess Adelaide's passing. Though the family's legacy died with her brother Eudes I (Otto) "the insane" as the legitimacy and honors of the Carolingians passed through the male line according to Salic Law.
Though knowing this, Napoleon II would probably be quite worried about the future of his dynasty and would probably try to entrench its roots within French society and maintain its relevance and position among the rest of Europe's royalty. Though unlike with Napoleon who father was impoverished minor noble from Corsica, Napoleon II is the grandson of Kaiser Franz and Napoleon I the man who nearly conquered Europe.