saying to someone we give them carte blanche means we give them full authority to accomplish a goal we gave them to do. They can do whatever it could take to achieve it, we trust they will be able to do it. (speaking as a french person) We do say "i give you (je te donne/je vous donne) carte blanche. Or "You have (tu as/vous avez) carte blanche.
Hope that might help
Where's the confusion? Carte = card, blanche = white.
White card, as in blank cheque (one that can legally be cashed but specifies no amount).