In 1879 in a war against the Zulu, Napoleon IV, son of Napoleon III participating in the British army met his maker. The question is why wasn't he part of the French army?
After the 1870 war his father's empire was abolished, and Napoleon IV went first to Belgium then to England. There was talk of him marrying one of Queen Victoria's daughters and the latter was in favor of it. He enrolled in some British military academy but I still find it odd that the British would let the most credible claimant to the French throne join their army.
Moreover, the Wiki article makes no mention of why he did not return to France. Perhaps he was banned from France but I doubt that. Still, I think it would have been better for his career to join the French army. Maybe the French army was in shambles after their defeat in 1870, I don't know.
EDIT: Precisions by @totalmongot
The closing reason is unclear. The OP in the question does mention points that are not "too basic" or answered by the single wikipedia article on Napoleon IV reading. Theses points are:
- Why did Napoleon IV not come back to France?
- Why did the British let him enter their army?
First point might find answers easily by googling, but not the second point. Because the second point is answered by the evolution of geopolitical context during 19th century, which is typically what an answer on SE could explain (since the OP is making the false assumption that Napoleon IV and Napoleon I had same feeling towards Britain).