Are you on the latest version of Fairphone OS? Check Settings > About phone > Build number to find out. I think your problem was mentioned before and then reported as solved by a recent update:
However, if you can hold out a little longer, I would recommend to wait until the next future update and not install the most recent update (it triggered NFC and Bluetooth issues). As a workaround until then, you might want to install a third party camera app (e.g. Open Camera) and see if that allows you to take and save photos right now.