Hi and welcome to the community forum 
I think a factory reset is unlikely to help, but it will have to be tried. The factory reset allows you to remove all the apps you’ve installed, and return settings to their default values. It is however the first thing that most professional repair services would do.
To my mind, if both mics stopped working at the same time, the problem is more likely to be linked to an audio hardware component that you cannot repair by changing a module, but it might just be a problem with some internal contacts.
A short-term approximation is to perform a cold boot in “Safe Mode”.
I would proceed in the following order:
- Make sure you have backed up (copied to at least one other device) all your data. This MUST be done first, because the phone is likely going to be reset, and that will wipe all your data. Given the state and age of the phone it’s a necessary precaution too.
- Turn the phone off and then start in Safe Mode. Test.
- Disassemble the phone and clean all contacts (battery, battery compartment and those of the modules themselves) with cotton buds soaked in surgical-grade alcohol or isopropanol.
- Allow several hours to dry before reassembly and testing.
- Perform a factory reset and test again.
- If you are in the area of a Fairphone Angel (see map) you could ask their advice.