Giving someone free reign. It sounds like it makes sense, but it's wrong.
It is if it's been spelt reign, however not if it's been spelt rein.
Free
rein is from horse riding and means to ride with slack
reins, the reins being the leather straps that the rider holds and that attach to the bit in the horses mouth. Free reins implies allowing the horse to do its own thing in the direction it takes, as opposed to tight reins, ie the rider controlling the direction by applying pressure through the reins to the bit to turn the horses head in the direction you want it to go.
So to give someone free rein implies allowing them to do whatever they please.