Hello, all.

After installing the acceleration pack, I noticed that the dialogue for the many of the airline missions and the Paris Airshow Demonstration Flight, were all missing. In fact, it seemed that FSX didn't recognize that the mission was taking place at all- after pressing Escape, the "Mission" dialogue box did not appear, but the free flight box did. As far as I can tell, all files are intact. What might be wrong?

Sounds like corrupt mission files or the Acceleration addon library objects folder. Steve's advice sounds spot on, run a repair.
The one reward you will not receive is the Eiffel Tower snapshot because of a longstanding glitch within the RWD file but you will receive a reward for completing the mission.