The blue "large family" (famille nombreuse) card allows you and your family to use half-price tickets on the public transport networks in the Île-de-France region.
There is a fee for this card: to apply for the blue "large family" card, click here.

The red "large family" card does not allow you any fare reductions on the RATP network. It is marked "non valable sur le réseau des transports publics en Île-de-France" (not valid on public transport networks in the ÎIe-de-France region). It does allow you to use reduced fare tickets on long-distance train lines (SNCF only).
There is a fee for this card: to apply for the red "large family" card, click here.