Is there a need for French teachers in Thailand?
If you were a licensed/certified educator, you could find a few job openings with international schools in Bangkok. A few of the bigger/better schools do offer French courses and teachers are well-paid (true expat salary). Although some of these schools may hire a teacher who does not have a degree in education (if in dire need), it would be a shot in the dark. That said, it may pay to search the schools offering French and make some 'cold calls' / send some 'cold emails'.
Since you are fluent in English, you'd probably find it easier to get hooked up with one of the many language schools around Thailand. They always stress 'native speakers' but I'm not entirely sure just how strictly they follow this.
Do you enjoy teaching? Can you see yourself being a successful teacher? If you have a degree in an area of media editing/writing... you may also find work at some universities, but be warned that most pay very poorly.
It should be noted that I'm a former Head Teacher / Head of Department (English & Humanities) within the international school market, and so my actual experience outside of mainstream education (overseas) is limited to 2 years of language school teaching way back in 1986-1988! I do, however, have extensive experience within the international school system of Thailand.
Good luck to you!