Every resident of Europe would receive an equal number of fossil fuel emissions permits, which he or she could sell to brokers at whatever was the going rate on the day.
Companies that bring fossil fuel into the economy would need to acquire enough of these permits from the brokers to cover the emissions from the fossil fuel they sell, and surrender them to the authority.
The number of permits issued each year would reduce in order to keep within the capacity of the atmosphere to handle carbon emissions, thus the value of each permit would rise rather than the price of fossil fuel.