TRIADE is an open-source school management system and virtual learning environment (ENT) for educational institutions, from primary school to higher education. It covers grades, homework and class logs, school life and absences, timetables, diaries, messaging, canteen and internship management, among other things. It is web-based and runs on PHP and MySQL. The project site also mentions optional components, such as an AI assistant (TRIADE-COPILOT) and custom modules (TRIADE-DEV). TRIADE is installed as server software by the school itself or by a partner.
TRIADE is published by a French project of the same name; its legal notice does not state a registered seat. The software is licensed under the GNU GPL v2 and the code is on GitHub. You can host it yourself, so that pupil and grade data stay on your own infrastructure. Note that the project's privacy policy states that the team may collect general information about the institution and about usage (telemetry). Check this before deployment, together with your data protection officer.