All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
The basic principle is that the Muslims (in a given community) should gather in one mosque to hold the Friday prayer in congregation; this was the Sunnah of the Prophet because the rationale behind holding the Friday prayer is for the believers to come together and strengthen the relations between them so as to maintain mutual compassion, kindness and affability among Muslims, as enjoined, in the first place, along with other purposes. This is why the majority of scholars held that it is impermissible to hold more than one Friday prayer in the same community except in case of necessity. They brought forth examples on valid necessities in this regard such as long distance, narrowness of the mosque (that it does not encompass the worshipers), and fear of potential fitnah (temptation, tribulation).
We believe that there is no need for holding the Friday prayer in your school as long as the mosque is near, as mentioned in the question. If there is a justifiable fear for the students’ safety and incurring harm on them if they go out of the school, then there is no harm in holding the Friday prayer in the school - if it is obligatory on them to attend it - given the necessity. If attending the Friday prayer is not obligatory on them in the first place, as is the case with young children who have not yet reached the age of puberty, then it is invalid for them to hold a Friday prayer for themselves, regardless of whether that be inside the school or outside of it.
Allaah knows best.