To be pedantic, it's possible to reduce carbon by using more efficient electrical processes even if you use the same fossil source e.g. burning gas to heat a home can be nearly 100% efficient, but electric heat-pumps can be up to 500% efficient which is still a positive if you burn the gas to generate electricity.

Also, I'm not sure why it's a popular semi-contrarian position to support new nuclear, it's it's simply cheaper to pursue other options like wind and solar and demand response etc.