Carte blanche (originally without “carte”) entered the English language as a French loanword in the mid-17th century, when card games were all the rage. A highly fashionable game of the time was piquet, in which a carte blanche was a hand having no face card.
By the 18th century, the meaning had expanded to include a blank piece of paper which someone signed, trusting a second party to come up with the stipulations of a deal. This idea of signing a yet unwritten contract and handing over authority to the other party led us to the sense most familiar to speakers of modern-day English. Nowadays, if someone has been given carte blanche, it means that the person is free to do or say whatever they please.
Note that it is a mistake to say “a carte blanche” unless you are talking about a piquet hand or a blank, signed contract. When used in the sense of giving someone free rein, you say the person has been given “carte blanche,” and not “a carte blanche.”
On the other hand, blank check, a term with very similar meanings, is always used with “a” or some other determiner. That term underwent the same progression as carte blanche from its literal meaning to a figurative one (as in Congress gave the president a blank check of unconditional support ). Unlike carte blanche, however, the literal meaning has not fallen out of use. We may rarely play piquet today, but we still occasionally write checks.

Did you mean carte blanche?