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This is a parallel reasoning question. This is how I understand the logic of the problem:

If one teaches in the French Department to which Professor Alban belongs, one cannot teach more than one introductory course in any one term. If the only language classes being taught next year are not introductory courses, both the French classes Professor Alban will be teaching next term cannot be introductory courses (at most one).

This argument seems logical to me.

I eliminated answer (C) because it does not follow logically. This is where I am stuck. I am not sure how to eliminate the remaining answers to arrive at the credited response.

I would like to thank you in advance for any help you may be able to provide to come to this solution.

The argument is logical, but your translation of the second sentence is erroneous. That sentence:

The only language classes being taught next term are advanced ones.

Properly translated: All language classes next term are advanced ones.
If/then format: If a language class is taught next term, then it is an advanced one.

This is your translation: If the only language classes being taught next year are not introductory courses

This introduces a conditional statement that is not present in the original stimulus. From the original, it is known that all language classes being taught next term are advanced ones. From your mistranslation, it is not known whether the language classes next term are introductory or advanced: thus your incorrect parenthetical remark that "at most one" of Alban's French classes could be introductory. Neither of Alban's French classes next term can be introductory.

As to the parallel reasoning aspect of the question, note that each premise independently proves the conclusion. Alban cannot teach two introductory courses in one term, per the first premise; neither can he teach an introductory course, per the second. When examining the answer choices, look for the one whose conclusion is proved by either of two independent premises.