If the Chrome workaround does not solve the problem, you could try this:
- Uninstall Firefox (back up bookmarks first)
- Reinstall a version of Firefox that Avast recognizes (version 52.0.1 is reported to work)
https://ftp.mozilla.org/pub/firefox/releases/
- Install Avast Passwords via the standard procedure (Privacy → Passwords)
- Test to make sure it works
- Update Firefox to the latest version