Hello there, the only legal requirement when traveling abroad inside the EU (whatever you are a EU citizen or not) is that you need to have public liability. Sometimes your home insurance policy covers you all across the EU (as personal public liability is always included on home & contents insurance in France) but sometimes not and also your kid may not be part of your property insurance anyway. As public liability is included on “schengen insurance” policies that may be a good reason to get one but apart from this one just asking for an European medical cover card (carte Européenne d’assurance maladie) is often good enough. Sometimes schools may require the “private” insurance too so it’s not really a matter of what’s legally required but what “they” may require from her 
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