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