I think you are going to struggle here. Michael is correct, it's likely to be 0.8mm pitch or similar fine pitch (0.5 or 1.00mm), however from a connector point of view the issue is that the FPC contact section is not square, it has the additional area. Generally FFC connectors have a closed end at each side and fit perfectly with FFC or FPC in a suitable thickness and a specific number of contacts.
So for example, you might have 26 contacts and you would find a 26 contact connector of the correct pitch, orientation (straight or right angle) and accepting the appropriate FFC/FPC thickness. However, to my knowledge connectors will only accept 26 contacts as they have fixed sidewalls and will not accept the extra dimension that the piece of FPC adds on one side.
FYI only Digi Key list 66 0.8mm pitch connectors but you can see it's not a popular range and not stocked. As a point of reference Digi Key have over 11,000 FFC connector choices.