The correct option is
A He does, but she doesn't
The question asks whether Mr. and Mrs. Smith speak french. The possibilities are that they both do or don't or only one of them does. The answer must indicate one of these. Further, the auxiliary in the question is 'do' and so the answer must also utilize the auxiliary 'do'. Also, the answer must contain noun(s) or pronoun(s) that refer to the subjects collectively or separately.
Option A is correct. It indicates that Mr. Smith speaks French and Mrs. smith doesn't. Thus, it indicates one of the possibilities, it uses the auxiliary 'do' and it has pronouns to refer to the subjects. It meets the required conditions and is correct.
Option B is incorrect. It utilizes the auxiliary 'to be' in the second clause instead of 'do'. Thus, it is incorrect.
Option C is incorrect. It utilizes the auxiliary 'to be' instead of 'do' in the second clause. Thus, it is incorrect.
Option D is incorrect. It utilizes the auxiliary 'to be' instead of 'do' in the first clause. Thus, it is incorrect.