What sort of ruler is he likely to be and what are the largest butterflies?
Well, he spent almost as much of his life in England as he did in France, so I would say he's probably likely to be Anglophile (like his dad). However, he
won't marry Princess Beatrice, not because of anything crazy like her converting being an issue (her mother was rather fond of him) but Victoria didn't
want Beatrice to get married, point. She made Beatrice and Henry of Battenberg sign an agreement that they would stay with her after they got married. Also, Eugènie, while fond of Beatrice, and godmother to her daughter, was more in favour of a Spanish match and IIRC the Prince Impérial was slated for one of Queen Isabel II's daughters, but then she died and then he died.
As to his policies, depends. If the Franco-Prussian War happens, and France still loses Lorraine, but keeps the Empire, he'll be a military minded leader (far more so than his father, more like his great uncle) at the head of a nation screaming for revenge, but hopefully he can avoid the worst excesses of the Republican regime. He's going to have to learn how to walk a pretty fine line since as a contemporary saying went "a shout from Paris and your hat (crown) flies off". With a marriage between the Prince Imperial and a Spanish infanta, he
might (bolded, underlined, in inverted commas) be
adopted by the Comte de Chambord. No shit, this was an honest to God plan between the Comte de Chambord, Queen Isabel II and Empress Eugènie. It would establish the Bonaparte-senior Bourbon line as the
legitimate rulers of France. Chambord would prevent the Orléans princes from succeeding him and France would still get a "liberal" regime (avoiding a Carlist ruler).