An French teacher may be one of the 2 categories:
Teacher of French
The technical differences are extremely small and yet valuable when making your decision. French teacher teaches French to French speakers, when a teacher of French teaches French as a second or a foreign language.
Unlike a French teacher (or a teacher of French) a tutor usually doesn't have a college or university degree in teaching, education or linguistics.
Tutors often use unconventional and more cultural methods of teaching. tutors tend to focus on student's experience and language natural development rather than typical books.
A teacher can teach you grammar, structures, time tenses and a tutor can help you expand your vocabulary and dip your toes into culture, however...
Practicing with a French Native Speaker helps you improve on pronunciation and understanding of a fast, real, dialectic speech, which is so different in France, Quebec, Belgium and other.