The EU supports agricultural policies to help farmers meet the challenges of climate change (CC) by promoting more sustainable and environmentally friendly practices. This study focuses on the European primary sector (agriculture, forestry, and fisheries), productive activities that meet humanity’s basic needs, although this sector does not account for a dominant share of GDP. The analysis uses a panel data sample of 22 European countries for the period 2012–2019, and seeks to answer the following research questions: Is there a direct relationship between agricultural innovation efficiency and the technological advances implemented? What effect do GHG emissions and innovation efficiency have on CC? Which agricultural practices have the greatest effect on the volume of GHG emissions? The results indicate that the European primary sector has registered an average rise in productivity of 4%, mainly driven by technological improvements. This underscores the need for agricultural innovation policies that focus not only on improving aspects related to technology but also on making better use of existing resources. In addition, the econometric models estimated confirm that efficiency levels are the most influential determinants of temperature change, while GHG emissions are primarily explained by their own historical values. Ultimately, research and development is a tool that can be used to curb CC, along with the proper use of land and fertilizers. There is thus a need to foster novel agricultural practices that help reduce emissions while ensuring the efficiency of the sector.