I would say one for Flybe.
The winter schedule is looking tight believe it or not but I am sure they could fit a daily flight in.
With the apparent back peddling by Flybe regarding the withdrawal of the E195 from the fleet (extension of the bucket and spade flights from SOU into the winter) I would have though that even if capacity is tight at the moment, the retention of an additional 195, perhaps deploying it on BHX-CDG, freeing up a 175 for BHX/TXL - perhaps even twice daily at business friendly times (AM and PM) Monday to Friday would be a possible option.
Group Lufthansa have made a right royal mess of their European operation - certainly on business routes - I'm sure that it's not only BHX routes on which 4U are struggling - and ex UK, BE are well placed to fill the gap properly, as they will surely do on BHX-HAM.