When someone parks on a car park they automatically enter into a contract with the owner of that car park to pay the charges which are displayed.
HOWEVER . . .
no contract can be entered into where one of the parties has not been made fully aware of the terms which the other party wishes to apply to that contract. A court would be likely to rule that, through not displaying the Saturday parking charges CLEARLY (especially when there's a far larger sign apparently implying that weekend parking is free), the operator of the car park has failed to provide the necessary information for a valid contract to be established.
Well over 90% of the posts here about car parking charges are from people who've not got a moggy-in-Hades chance of getting the charge withdrawn. However, based upon your description of the signs, your friend seems to have a valid case for a successful appeal (with the car park operator having little chance of winning in court if they decided to reject the appeal and sue your friend).