I don't understand how you reached the conclusion that PAR/ORY is the problem? By that logic, why is NYC/JFK not the issue?
There is logic in that ORY-LIS-JFK could be not available as an award, while the independent segments are available. It fully depends on how the operator publishes their availability. I believe that this phenomenon is called married-segments.
However...as you tried to book online as well (?), I would assume that the website showed availability for the full itinerary. So that would indicate that there is availability?
Perhaps call again, another operator may be able to book it for you..