in that case the easiest thing is to arrive and get a 30 day exempt tourist visa and pay the 1900 THB for a 30 day visa extension and that way you get your 60 days
The issue is that you and your family are possibly not French nationals but from a third country which has no visa on arrival arrangements with Thailand and so all applications are vetted via the Royal Thai embassy in your country of origin and it does take longer to process
there are a lot of Thai people who speak English and will always offer to help. Language should not be a major problem really, and if you go to a hospital whether private or public you will always find English speaking medical and nursing staff. Thailand is not China where language is a real problem
Also something particularly useful is one of his mates here in Australia making an affidavit confirming they are aware of their relationship and that they plan or that he plans to bring her for a visit to Australia for a certain period of time and that (the friend writing the affidavit) knows this to be a bona fide relationship and that she will be coming as a genuine tourist/visitor for the purposes of getting formally introduced to his family and that she has no intention of overstaying. The more affidavits and letters of support the stronger her case.
A supporting letter or affidavit from her Australian partner and also from his family confirming she is coming to visit them always helps, especially if they state that they will be financially responsible for her visit to Australia