With the increase in global geopolitical risks and the frequent occurrence of extreme climate in recent years, the electricity prices in Europe have shown large fluctuations. Electricity price has an important impact on the cost of production and living, while electricity demand will also affect other energy markets. A double-layer system based on the spillover effects from a systematic perspective is constructed in this paper to explore the connectedness between different electricity markets and other related energy markets in Europe, considering the impact of climate risks. The results show that there are certain spillover effects among electricity markets in different countries, with a temporary upward trend in the beginning of the Russia–Ukraine conflict, and the electricity markets in the UK and Germany have a more important role in Europe. There are two-way spillover effects between the electricity market and fossil fuel markets, carbon market and carbon emission. Since 2022, the electricity market is affected by gas prices, while it has a certain impact on carbon emissions. The heating degree day (HDD) has significant spillover effects on the electricity market and other energy markets, while the spillover effects of the cooling degree day (CDD) are relatively small.