City Jet not very likely
I only think City Jet would be allowed to operate as an AF brand which means CDG. Interest from AF to do this route is not likely to be too high.
I suspect Fly Be are doing okay on CDG but not ready for competition if any on this route. I can't see the CWL management team offering City Jet a deal for CDG.
LCY would be a very strange move as there is a train every 30 mins to London and the other option of DUB would be mentally stirring a hornets nest at FR and EI. Again can't see CWL management doing any incentives on this either as RE have been saying they will increase capacity on this route.
Could be the City Jet pilot was getting confused as they could be operating some flights on behalf of Fly BE, like have recently been happening with other BAE146 operators.