DIALANG is a free language diagnosis system available from Lancaster University. It reports your level of skill against the Common European Framework (CEFR) for language learning. DIALANG languages are Danish, Dutch, English, Finnish, French, German, Greek, Icelandic, Irish-gaelic, Italian, Norwegian, Portuguese, Spanish and Swedish. DIALANG has instructions and tests in all these languages. Competences tested are reading, writing, listening, grammar and vocabulary, speaking is not tested. Appendix C of the CEFR contains the descriptors for self-assessment at series of levels adopted by the DIALANG Project of the European Commission for use on the Internet.
You will probably find more free tools online for specific languages, here for French for example, that that will be more appealing to young learners but none are as elaborate as Dialang which was funded by a European programme.