Just an update on the Champs Elysees property in Paris. I emailed them with the email address on their website and explained the problem. Received an email back the same day stating that the availability is now there and open for me to book.
So, as usual, contacting the property directly worked in this situation. That said, 97% of Club Carlson members would probably just assume no availability means no availability, so it still is pretty crummy that you have to work with the property directly to book what you should just be able to book.
Glad they were responsive though.