Hi Luc about 3 years ago I was in the boat you are now in - wanting to do the training but unsure that I would be a good teacher. Due to personal circumstances I was not really seeking a paid overseas position. I ended up doing a TESOL Certificate (Teaching English to Speakers of Other Languages) - training with Teach International (originally from NZ but now based in Brisbane Qld). The course was both on-line (80% pass marks) and a five day face to face training which included giving a 45 minute presentation. The course also required between 4 and 10 hours face-to-face (real students). Since obtaining my certificate I have done two stints of overseas teaching (as a volunteer) in Tanzania.
So basically I would say - go do the training, pick one that involves class room preparation and lesson planning and delivery techniques. Most community colleges offer ESL training to newly arrived people and this may provide an opportunity to develop your training/teaching skills before heading off overseas.
Sites that may provide avenues for paid employment include "www.daveseslcafe.com" (do a google search). Countries that still have paid employment include Vietnam (usually 3-6 months period required); Cambodia - but I think these require around 6 months. South America was a good option - but I understand most schools require you to have some Spanish language skills and again sign up for 6 months to a year.
Go for it and good luck. O_M