Philologists say, that it is actually "War and world" with "world" meaning "the people". And it makes sense since the book tells us about how people's lives get affected by the war, and not so much about peace. In the times of Tolstoy these words had different spelling, but in modern Russian they're the same.
I don't know about philologists, but the word мир (mir) used to be 2 words, spelled differently under the pre-reform Russian alphabet.
Война и миръ (wojna i mir) is the original spelling of the title.
миръ (mir) meant only "peace," but there was also:
міръ (mir) - world, universe.
The two were pronounced the same, and "і" was dropped from the Russian alphabet. (It's still used in Ukrainian and Belarusian.)
So according to this, the title was War and Peace originally. But I'm sure Tolstoy still meant to play on the double-meaning since it was a homonym