I look at reserve as to place something on hold ("I reserve a hotel room or a table"), or to intend to borrow ("I place on reserve a book from a library" ) usually at no cost. To say I "book" usually implies payment in exchange for a guaranteed space. "l booked a flight, ticket or room" Hope that helps
Can I wade in with my 2 pence worth here... I would suggest that when you "book" something that it does not necessarily imply in exchange for payment. For example if I called a restaurant to reserve a table for me and my wife, I would either tell her "I've booked a table" or "I've reserved a table", and I would suggest that both mean the same without any implication of payment having already been made or not. Not sure if this is more a local thing where I'm from but I would certainly argue that both mean exactly the same.
The reverse tree is the course teaching English to French speakers.