Do you want to teach just English or become a primary school teacher here in France?
For financial reasons English in primary schools is now taught by the students’ regular teacher. To teach in primary schools you have to pass the CRPE (concours de recrutement de professeur des écoles). The following sites should be helpful.
Concours de recrutement de professeur des écoles - Wikipédia Professeur des écoles - Wikipédia
The fact that the vast majority of these teachers don't speak English didn't seem to be a problem for the decision makers!
To teach English as a subject in either a collège or lycée you’d have to pass the concours du CAPES (Certificat d'aptitude au professorat de l'enseignement du second degré). I think you have to have either French or European nationality.