Try clearing Free Fire cache. Go to Settings > Apps > Free Fire > Storage > Cache > Clear Cache. Another advice is to use a fast network connection - slow networks may cause issues in the game. Switch between 4G/5G/WiFi.
If you still obtain the "Authentication Failed" message, restart your phone. And as a last resort, uninstall and reinstall Free Fire. If you use a guest account, reinstalling the game will erase all of your progress. To avoid this, please bind your account.
Hope that will work.