The reason we (UK) use French spellings is because we were invaded by French speaking Normans. After the initial cultural shock, it became fashion to "Frenchify" the language. Whether this was a genuine appreciation of French culture or a desire to ingratiate the new rulers, I'm not sure. Spellings such as "centre", "colour", "hotel" were adopted, even though they are still pronounced like "center" and "color". Many loanwords were adopted, such as mutton, beef etc. Some words were adopted twice with different spellings, e.g. warranty and guarantee, hotel and hostel.
Many words in politics, law and the military are derived from French, as the Normans took key roles in all those areas.
Not just spelling, but also names. Traditional English names like Ethelred disappeared, replaced with Thomas, David, Henry etc. Normans also introduced the idea of surnames. By default, people were named after their occupation, so "Smith" became the most common surname.
It's somewhat ironic that modern Brits often disparage the French, but we were hugely influenced by the Norman invasion. Although, Normans weren't native French either, they were occupied and then ruled by Vikings that settled in France. (Norman = Norse-men, literally "men from the North").
Anyway, I actually prefer the US spellings, they make more sense. Also, the US spell checker is often the default, so it is easier just to use that.