Restore Firefox & Thunderbird user data from Time Machine
The User Data folders for Firefox and Thunderbird are:

/Users/$USER/Library/Application Support/Firefox
/Users/$USER/Library/Thunderbird


You might also want to migrate the .plist files for them as well:

/Users/$USER/Library/Preferences/org.mozilla.firefox.plist
/Users/$USER/Library/Preferences/org.mozilla.thunderbird.plist


Make sure the applications are close before migrating the folders/files.