Truth is both sentences can be used in French : - "Je suis professeur" : where "professeur" is used as an adjective, a qualifier. This is the common way to specify your job, your nationality : "je suis français"; - "Je suis un professeur" : where "professeur" is used as a defining criteria of "Je". This is the common way to read a definition in the dictionary : "Le lion est un animal" or possibly introduce oneself "Qui suis-je ? Je suis un professeur."; - "Je suis un professeur [...]" : where "professeur" is part of a greater group or is to be additionally qualified, etc. If context is given we would have examples like : "Je suis un professeur parmi d'autres", "Je suis un professeur à l'université de Lille", "Je suis un professeur en formation", etc. I hope it helps!
In French (and Spanish) the definite article (the a) isn't used. In English, we say he is a professor but in French, we say il est professeur.
However if someone were to ask you Who is that man? and you were to answer He is THE professor you'd translate that that as Il est LE professor.