Mark Twain hated the puffery and inherited wealth that the European societies welcomed. In his first popular book, "Innocents Abroad", Twain poked quite a bit of fun at the European traditions of honoring the past and their class society. He continues this tradition in "The Adventures of Huckleberry Finn." The King and the Duke make up brazen stories about their heritage but they are nothing but con men bent on the destruction of the Wilks family and others misfortune. He refers to the French dauphin, the heir to the throne, as a "dolphin" and gives the Duke the name of Bilgewater which is waste water dumped off a boat or ship. It is obvious Twain has no use for the pretensions of Europeans or their royalty as seen in the eventually end of the "king" and "duke". They are both tarred and feathered and led out of town on a rail. Thus, Twain uses the Europeans to satirize all inherited wealth and their pompous behavior.
In Chapter XXVI, Huck explains to the harelip that slaves "ain't nobody" in England. Ironically, slavery had been abolished in England in 1833, shortly before the time of the story. Readers would've been aware of that irony.
In Chapter XXXV, Tom says that Jim wouldn't understand "European ways" which include sawing off a hand to escape chains. Again, it's ironic because slavery had been abolished already in England, Portugal, Scotland, France, Spain, and other places in Europe.
I would also go so far as to say that Twain thought that European values and ideals were the causes of the American Civil War. You can see it in Tom's character in the lengths he goes to conjure up adventures and in his Romantic notions of what adventure is. It seems that Tom's adventures are based on European books of lore.
This probably resulted in a misguided view that war is romantic, war is exciting, and that war is "fun," but with devastating consequences. You can see that in the death of Buck as Huck cried for the first time in the noel, I believe.
From a heavy influence of European allusions from the Walter Scott to the dauphin, from the King and the Dulce and their Shakespearean revival to the books that Tom references, such as The Count of Monte Cristo, one can see that twain had an uneasy feeling concerning the influence of Europe in an unsettling time for America, the Reconstruction after the Civil War.