I went to school in french speaking Belgium, but it’s the exact same in France. At age 11-12 (depending when your birthday is) kids move from the primary school (école primaire) to the secondary school (école secondaire). It is in secondary school that children start to address teachers with Professeur, simply because many teachers in secondary are actually professors, that is to say, they went beyond a master’s degree and got a ‘doctorat’ and became professors. Most of our physics and math teachers in secondary were actual professors (people with a PhD). But you simply address everyone with professor in secondary. So you have Professeur de collège, Professeur de lycée etc. There’s no such thing in primary school, we never addressed a teacher with professeur until we were in secondary.

I speak for France, I have no experience of other french-speaking countries.
The terms “maître” and “maîtresse” are used in primary schools, that is to say from the CP (cours préparatoire, usually 6 years old) until the CM2 (cours moyen 2, usually 10 years old). As said by Greg, primary schools teachers are officially called “professeurs des écoles” but pupils usually call them by these names.
In higher education, i.e. secondary schools (collèges and lycées) and universities, you usually use “monsieur” or “madame” to address a professor. I have personally never used “professeur”.

I’m teacher in belgian secondary school.
In primary school (6-11 years old), the pupils call ” Madame/Monsieur” with the first name or family name.
Officially they are “instituteurs”. They have studied during 3 years in high school.
In secondary school, (12-18 years old), the pupils call “Madame/Monsieur” with the family name but between them they say “Mon prof de” + matière OU “Madame/Monsieur” + family name.
But officially we are “enseignants”. For the 1st-2d-3d level, we can go to the high school (3years) or to the universities (5years). For the 4th-5th-6th level, we can only go to the universities (5years).
We are not PhD.
In universities, they are called by students and officially “professeurs”. But there are also “assistants”, who are not professeur but can help students. They are PhD after few years and when there is a “place vacante”.