In French a different noun for "student" would tend to be used according to the type of school attended. For students in high school or below that level the term "élève" is used the most; for students in university, the word "étudiant" is used almost uniquely. The following terms are common.

• élève moyen, étudiant moyen (ngram)

The term "bon élève" is used a lot also, but "bon étudiant" is not used much. (bon).

How you render an "B student" in French depends to what purpose you need to use the phrase.

• If it is to be used in a casual manner and do not need to be accurate you could say:
  • • un élève/étudiant tout à fait moyen

which is a phrase teachers and lecturers would use when talking about a student who is just above average (which is what a B student is).

• If you need the phrase for a more formal situation, for instance for a cover letter or to apply to a French university then you might have to give a numerical rating equivalent using a converting table (as the one you can see there). But in fact if you apply for a French university they will ask you for a transcript of grades from the previous academic year (whether in high school or as an undergraduate).

Note that this applies to France, in other French speaking countries they might express this differently.

France and US grading systems are somewhat different in both their range and linearity.

As you described B as "average", that might match un étudiant/élève¹ de niveau passable (enough to pass). This level applies to students with a grade between 10 and 12 or that might match a bon élève if the B level is considered to match the assez bien French one.

After reading all the comments, I believe the closest expression would be un assez bon élève.

Here is a chart where I try to match France and US gradings assuming B is passable² (third column) or, more likely, assez bien² (last column):

Sources:

1. French and American grading equivalency for transcripts: Why is it so hard to convert French grades into American grades (and vice versa)? – Charles Eddy

2. Ammon & Rousseau

3. Studying in France

4. Université Paris 10 – ECTS

¹ In France, we use élève for a student attending a primary school (écolier), a secondary school (collège: collégien, lycée: lycéen). Students attending a University are called étudiants. Students from grandes écoles (Polytechnique, ENA, Saint Cyr, Centrale, Mines, Pons, Normale sup…) are also often still called élèves.

² Note that on the meaning of a French grade might substantially vary depending on the level (primary, secondary, university, grandes écoles…), the school, the teacher, the period, the discipline or the kind of exam. The trend is often reported to be towards higher and higher scores for a similar level, and marks that were exceptional several decades ago tend to become commonplace.

Un étudiant ordinaire, …comme un autre.