Sounds an awkward situation!
Difficult to answer without knowing the detailed background. If the festival committee was set up by the council, then the problem would have to be referred back to the council. If it is an independent project, then it should be governed by its own constitution, which will determine whether you can take any action.
Either way, it might be worth approaching the chairman of the parish council to express concern that the council's representation on the festival committee is ineffective. Or, if it is easier, you could approach the council through the parish clerk.