While many languages make a difference between 'teacher' and 'professor', there are even more French words for teacher than there are English ones. The most common word for teacher in French is professeur, which does not translate directly to 'professor' in English. In French, a professeur can teach at an elementary school or at a university. In addition, the whole word is seldom used in its entirety; the common word is prof.
Several French Words for Teacher
The most common word for teacher is prof, but there are several more:
Each of these words has a certain connotation, and the rules for using each one are not as black and white as they are in English. In English, a professor teaches at a university, and a teacher teaches at a school. In French, the words for teacher are chosen more out of the context and the amount of respect that one has for the teacher instead of the place where the teacher physically teaches.
This word was traditionally used at schools for children of all ages. A beginning teacher might be called this, as the name implies that the teacher is doing a job of teaching students of some particular age. In contrast, the term maître implies that the person teaching the subject is a master of the subject.
This term was used more in the past than it is used today; however, the word is still a good choice if you want to describe certain teachers. One context in which this word is still frequently used is that of referring to an aging master in a subject. For example, if you are learning a fine art, such as wood carving, the subject is one that can be best taught by someone who has a lifetime of experience doing this activity. While a younger teacher may know all the 'rules' of the craft, many people who begin learning such a fine art will prefer an experienced craftsman. For this teacher, the term maître is appropriate.
Another, totally different, context in which this term is frequently used is the primary school. Teachers who teach very young children sometimes ask or teach their students to call their teacher maître when speaking to the teacher or when calling the teacher. You can see this term in context in the hit documentary Etre et avoir, which chronicles a school teacher in the countryside who has sole charge of his students though they range in age and intelligence.
Note that in some regions the term maîtresse is considered unnecessarily sexist. Much like mademoiselle has been mostly eliminated from usage, maîtresse is unfavorable in some regions.
Alongside the word professeur, these two (masculine and feminine) French words for 'teacher' are reliably good choices regardless of the context and the gender of the teacher. From the French verb enseigner (to teach), these words for teacher are neutral in connotation, meaning that they have no hint of either a positive (reverential) or a negative (school-marmy) connotation. As long as you remember to make this noun agree with the gender of the teacher you are talking about, this word is virtually foolproof.
This word for teacher is also a neutral one in connotation, and widely used both among teachers and among students. In contrast to the maître/maîtresse distinction that already existed throughout the history of French, the word professeur was always historically masculine in French. In recent decades, the word has taken a feminine article to refer to a female teacher; for example, one would describe their female math teacher as: ma professeur de mathématiques.
A further detail of note concerning this word for teacher is that the word is often shortened to prof in spoken contexts. Note that the male/female distinction remains: mon prof d'anglais et ma prof de mathématiques.
Whether you use these words for teacher to refer to your French teacher or your singing coach, try to choose the word that is most appropriate for the context in which this person is your teacher. When in doubt, go with professeur or enseignant(e), as these two are virtually immune to changing context and situations.