I believe Sweden had and still has a French family ruling. Usually monarchies have an order of succession for the country's people and the King's/Queen's family, right?
To have a foreigner on the throne was quite common back then, due to various royal marriages and family ties most rulers were connected to one another is some way. If you take the British royal family for example they are decended from a long line of German rulers.
But this is when the strange case of Sweden came about, it makes for some very interesting history. To see why a Frenchman was put on the throne we have to look at what Sweden was doing in the Napoleonic Wars.
At the begining of the Napoleonic wars Sweden was a pretty small power with a weak agrarian society and a small population of 3.4 million. War with a major power would likely prove disatorous and the then current king Gustavus Adolphus IV was wise in that he kept out of the French Revolutionary Wars and then joined the armed neutrality pact with Denmark-Norway and Russia. But his mind completly changed when he heard of when Napoleon executed the duc d’Enghien in 1804. From then on he would not stop until the "evil" Napoleon was dethroned forever. The Swedish were in the Third and Fourth coalition but did very little in the war and lost Swedish Pomerania. In 1808 with the prodding by Napoleon the Russians and Danish invaded Sweden and despite the efforts of the Swedish they lost all of Finland to Russia. The loss of a third of the nation's land and a quarter of their population was too much for the Swedish leadership and they deposed Gustavus Adolphus IV in a military coup in favour of his aging uncle Charles XIII.
Charles was frail at this point and his wife had given birth to two children but they both died in their infancy. He had adopted the Danish Prince Charles August but he had suddenly died probably of a stroke in 1810. It seemed that Sweden would soon be going to war again so the government wanted a soldier king so in a strange series of events Baron Carl Otto Mörner invited Jean-Baptiste Bernadotte to the Swedish throne. Bernadotte was one of Napoleon's marshals but his poor showing in 1807 and 1809 led him to being disavowed by Napoleon. In the war against Sweden Bernadotte had shown kindness towards the Swedish prisoners of war and was quite popular in Sweden and was soon elected by the Riksdag of the Estates. In 1810 Bernadotte and his wife Désirée Clary (Napoleon's ex-fiancee) moved to Sweden and assumed the title Charles XIV Crown Prince of Sweden and became the defacto ruler of Sweden. In 1813 he would go to war against Napoleon and was able to secure Norway to his holdings. In Febuary 5th 1818 he became the king of Sweden and his line still rules to this day.