Reddit reviews Latin Alive: The Survival of Latin in English and the Romance Languages

I really enjoyed Latin Alive. It's very readable and entertaining, with lots of interesting etymological connections. It follows the evolution of Latin up through early forms of French, Spanish, and Italian, but not all the way up to the modern languages.

You could start there, and if you wanted to go into more detail, you could try Romance Languages: A Historical Introduction, which is more of a textbook, so less storytelling, but it's still pretty engaging and accessible (at least the parts I've read).