OK, I've moved this into the French section.
If your mother is here on a 3 month visitor visa (usually referred to as a Schengen visa), then she can't renew while still in France.
You can only extend a long-stay visa (and even then, there are specific terms and conditions). If she wants to stay longer than 3 months, she'll have to return back home and apply for a long-stay visa at the consulate in her home country. What sort of visa she can apply for will depend on your status here in France, as well as her resources and intentions.
Cheers,
Bev