Time to pick a school. There are many options in Luxembourg, public and private. There are no tuition fees for the Luxembourgish state schools or the European school (in case one of the parents is an employee of the European institutions). Private schools do charge a fee of course, but are probably an interesting option if you plan to leave Luxembourg within a few years.
It’s important to take into account additional educational expenses when you’re comparing schools and systems! Think of extra-curricular activities like arts and sports – some schools offer them, some don’t. Check out the option in the “Maison Relais” of your village and speak to the Youth Association for more options.