Question: Why did Inspector Fix take sides with Fogg at the end of the film?
Question: When Passepartout, Phileas Fogg and Monique are looking at a map to find a way of avoiding the British police, Phileas notes that they can't go to Singapore or Hong Kong because they're both British Colonies. Monique asks if England owns every country in Asia, Passepartout says they don't own China. Since Hong Kong is located in China, shouldn't England own that as well?
Answer: Hong Kong was indeed under British rule from 1841-1997. In short, it stems from the First Opium War where in the aftermath of the war, China ceded (gave up control of) Hong Kong to the British. After the war, with the cession of Hong Hong, it wasn't technically part of China any more and Britain didn't really seek to occupy more of China.
Answer: He felt foolish for accusing Fogg and hounding him across the world, the least he could do is help him win the wager.
Not only that but, like Lord Kelvin's other associates, Inspector Fix was berated constantly by Lord Kelvin and was even thrown out of a window. Inspector Fix had got tired of Lord Kelvin's bullying and decided to tell the truth in front of everybody.