The Ir Binyamin explains why he was required to address them in Hebrew.
The Gemora below states: Rabbi Yochanan said in the name of Rabbi Shimon ben Yochai: Hashem is communicating to Bnei Yisroel that even if you only say Kerias Shema at morning and night, I will ensure you do not fall in their hands. [This does not mean they do not have to keep the other commandments, but rather that they do not have to study Torah during the war more (if they do not have time to do so) more than the minimum of reciting Shema every morning and night.]
It can be suggested that Rabbi Shimon ben Yochai is following his own opinion, for he says (Menachos 99b): Even if only recites the shema in the morning and at night, he has discharged his obligation of studying Torah day and night. And then he adds: It is forbidden to say this over to an am ha’aretz (ignorant person; for then, they will not study Torah; they will only recite kerias shema).
It is now understandable why the Kohen addresses the nation only in Hebrew. Since he is informing them that it is sufficient if they merely recite shema in the morning and at night, even if they do not study Torah the remainder of the day, he must speak in Hebrew, a language that the ignorant people do not understand.