The residential price of electricity is often based on the most expensive source, which is usually gas.
For example, in the UK we have a bidding system where suppliers bid to sell energy a day in advanced, based on predictions of demand. Their offers are taken up starting with the cheapest and working up the list to the most expensive, until the predicted demand is met. Renewables typically bid zero and are the first to be used, followed by gas. Nuclear has a sweet deal where we have to buy their overpriced energy no matter what.
Everyone gets the highest bid that was taken up, which is almost always gas. And thus the retail price of electricity is set by the price of gas.
The less gas we use, the cheaper electricity will become. Nuclear won't help because it gets guaranteed very high price, and new nuclear takes over 20 years to build. Renewables are the only way to bring down energy bills.
Don't make the mistake of comparing us with subsidized bills either. France has a low retail cost because much of the actual cost is paid from general taxation.