Public and private schools of Moscow often have an international vibe as they are often made up of students from a variety of countries. There are schools dedicated to specific languages:

BISM is an established educational institution. Dedicated, Native, English speaking teachers work closely with highly qualified specialist support staff.

Anglo-American School (8 Bol. Devyatinskiy Tel: 956-4204) is privately run by the American embassy.
Admission is from age of 6. There are classes that are only open children of the embassy.

Lycée Français de Moscou Alexandre Dumas
7A Milioutinsky per., 101000 MOSCOU Par la valise diplomatique : Lycée français de Moscou Ambassade de France en Russie 13, rue Louveau, 92438 CHATILLON cedex
Telephone : (7 495) 514.15.46
Telecopie : (7 495) 980.50.99
Email : lfm@lfm.ru
Pre-registration of new pupils is solely available on the Internet.

There is also a Finnish School (5 Ulofa Palme ul, 143-6179) which takes grades 1-9.
A German School (103 Vernadskogo prosp, 433-6061) . Private school run by the embassy of German. Accepts grades 1-12.
Italian School (38 Lobachevskogo ul, 431-4966) accepts grades 1-8 and has a kindergarten.
Japanese School .( 78 Leninskiy prosp Tel: 131-8733)For children of the embassy staff. Accepts grades 1-9 grades.

For a continued list of schools: forum.expat.ru/phonedir.php.