Fossil fuel usage will decline as better alternatives become economically viable.
If you add to the cost of fossil fuel the damage they do that time will come much sooner. If my neighbor builds a house by piling all the dirt on my property it will be a lot cheaper for him. If someone burns fossil fuel and warms the planet they don't personally bear the costs. Proper treatment of what economists call "externalities" has to be the job of society in the form of the government. That's what a carbon tax is all about. We solved acid rain at much less costs than anticipated. The miracle of the market really can find the best solution if the costs of externalities are factored in properly. We'll probably never get to zero use of fossil fuels, but we can get to much much less. The pope has done a service by pointing out that it's our moral imperative for the future. Now if only one party would stop saying "we're not scientists" we could make a lot of progress.