What is the ruling on preventing the group "Going forth in the path of Allah" from entering the mosque in a French village, given that the mayor threatens to close it if they are received, and should they be prevented or is it impermissible?

Muslims must keep the mosque open and not subject it to closure. The Tablighi Jamaat can stay in homes, and if it is possible for them to pray and study in the mosque during prayer times while their official residence is outside it, that is preferable. Otherwise, their meetings with people should be in homes, clubs, and cafes. One must supplicate to Allah to rectify the affairs of Muslims and be keen to avoid discord and conflict within the mosque community. Remember that the Prophet, peace and blessings be upon him, used to meet people in the house of Al-Arqam in Mecca.