I think the rule is that each person has to apply for their own visa - and only children under the age of 7 or so are exempt from having to appear in person. The fact that your granddaughter is not part of your household just makes it all the more important that she apply on her own.
When her mother joins her, will her father be coming, too? Because, if so, both mother and daughter will be covered as non-EU family members of your son-in-law. In that case, your granddaughter would probably only need a "visitor" visa - though I'd make it for a little longer than 6 months, just in case there is some delay in her mother and father moving over.
When you say her mother has an "EU card" - what does that mean, exactly? If it's an EU passport/nationality, then no problem. But if it's a carte de séjour (or similar) based on her husband's EU nationality then she will have to be "joining" him in France to be eligible for the carte de séjour as the spouse of an EU national.