To synchronize Google Contacts with Thunderbird I used Google Contacts in the past. It seemed that this add-on no longer worked for me with the newest Thunderbird version. So I looked around a bit and found a replacement which seems to work fine: gContactSync. The reviews for that add-on state that there are some bugs which might lead in deleting contacts from Google randomly. However, I only use it one way (my primary source is Google and I only write to Thunderbird) so it is not an issue for me.
Sychronize Google Contacts with Thunderbird