From what I know about teaching English is that you do not have to be a native speaker. It varies from country to country and company to company but if you are a non-native english speaker then you can still apply but you have to have certificates to prove your level and fluency. Of course if you have live in an English speaking country or been in a job where you use English a lot then this also helps...most require 10years or more experience but some places are a bit more flexible and normal make a decision through interviews.

Doing one-on-one teaching will be more suited although if french is your native tongue and you speak english as well it might also be worth considering teaching french to english people too

best of luck