If you haven't been following along, I'll give you the short version of the whole story, starting at the beginning. If you have, you can skip the next couple of paragraphs to the most recent part!
We had booked flights with Air France from Paris to Ottawa direct. When we went to check in, they told us the flight was overbooked, but they offered us €600 ($875 CA, $642 USD) each in cash to switch our flights to arrive in Montreal, with an Air Canada connection to Ottawa.