The Napoleonic Wars was a truly global war with a majority of the world involved, naturally Scandinavia would be involved. Up until the defeat of Prussia in 1807, Denmark was looking to stay neutral since they were both a major trade power in Eastern Europe but also served as a gateway to Eastern Europe, thus looking to stay away from both British, Russian, and Swedish influence which were active in their war against France. However, this wouldn't last long (in 1801 the British did attack the Danish in an attempt to end neutrality that was in favor of French trade, leading to a victory but hardened Denmark against the British) as Napoleon had defeated Prussia and became the major power in Central Europe.

The British had a problem, Prussia had fallen to Napoleon and Denmark is near Prussia. Fearing that the French would have a large navy that could counter the famous British navy (remember that France is a strong land power but never had the competence at sea as the British), the British preemptively attacked the Danish to ensure that the Danish fleet didn't get into Napoleon's hands. While it was successful in that, it hurt the British slightly in the long run in what is called the Gunboat War. With Denmark without a navy, they used small boats with a relatively low number of guns to harass the British and keep them at bay until 1814 when the Coalition forces were pushing West after the defeat of Napoleon at Leipzig.

On the reverse, Sweden came into it's own. For long, Prussia and Russia had been slowly chipping away at the power of the once mighty Sweden. For almost two hundred years, Sweden had gone from the main power in Northern Europe to a primarily regional power that never had gained the power of Russia or the trade of Denmark. However, being a part of the Coalition, it would try and fight France with the Allies. While not able to give a large contingent, say a brigade or so under the command of Prussian commanders, it contributed what it could. There, a small group of Swedish officers would be entertained by Marshal Jean Baptitste Bernadotte, whom would carry home his name as a good man and later these stories would become important for his nomination to become Crown Prince of Sweden. I have written some about Bernadotte here.

So Bernadotte would become Crown Prince in 1810, renounce his titles in France and move to Sweden to take his place. There, he would slowly turn Sweden against France and become an important member of the Coalition against Napoleon, educating the commanding generals on the finer points of Napoleonic Warfare and logistics as well as the importance of dividing Napoleon's corps to prevent him from having his full strength on the field.

As the Coalition pushed West, they would later push Denmark to accept a peace that would have them lose Norway to Sweden. From here, I cannot speak more but I hope this helps. If you have anymore questions, I will do the best I can.