Markets can only work, if the prices for something tell the truth about the costs of something. You won't solve that with just cutting subsidies for all energy sources.

And carbon emissions are not everything. The idea to reduce them by trading certificates collapsed in the minute when the total amount of certificates were not lower than the amount of carbon emissions in the past or when it was not adjusted for the solar and wind power which were build over time. If you would cut the amount of certificates in half and auction them off, it might work. Otherwise the market will fail.