The auxiliary verb 'did/did not' must be used before the verb. So, "study didn't/studies" in option A is incorrect.
"Didn't study/study" in option B is incorrect as there is subject verb disagreement in the second blank. The verb should be singular 'studies' to accompany the singular pronoun 'he'.
"Did not study/studies" in option C is correct as the conjunction 'but' indicates contrast. Thus, Geoffrey did not study is correct.  Also, 'studies' is correctly used for the singular pronoun 'he'. 
"Didn't studied/studies" in option D is incorrect as didn't studied is ungrammatical. 
Thus, option C is the correct answer.