Well what we should do to limit fossil fuel consumption??? What we should do is what humans usually do, namely 'cooperate by competing'. Cooperating by competing is the whole basis of Adam Smith's economics. I'm not suggesting the competition is individual capitalism. Rather the competition is over the rents associated with fossil fuels.
Let me explain. Fossil fuels are limited by how much is in the ground, but even more, they are limited by the desire to have a safe, non-hothouse Earth. If we want to preserve the natural world and the environment that we have grown used to, we need to limit the amount of fossil fuels that we dig up and burn. Any limitation has a 'scarcity rent' associated with it. Who charges the scarcity rent is up to us.
So the UNFCCC should give its official blessing to set up two cartels; a cartel of the fossil fuel producers, which would limit the amount of fossil fuels dug up, and a cartel of the fossil fuel consumers, which would limit the amount of fossil fuels burnt. Rental income from both cartels would be returned to the producers and consumers of the fossil fuels respectively.