Abstract Reducing greenhouse gas emissions in residential buildings relies on three channels that are rarely assessed together—insulating homes, switching to low-carbon heating systems and decarbonizing heating fuels. Their combination results from an interplay between top-down planning of the energy system and decentralized policies for the residential sector—insulation subsidies in particular. In this paper, we examine how the design of insulation subsidies influences the allocation of efforts between these three channels. To do so, we use an innovative framework coupling a highly detailed model of residential energy demand with a highly detailed model of the energy system, both focused on France. We find that the most cost-effective effort allocation to reach carbon neutrality implies 19% emission reductions from home insulation, 36% from fuel switch and 45% from fuel decarbonization. This however requires perfectly targeted subsidies. In three alternative, arguably more realistic subsidy scenarios, we find that total system cost is increased by 11%–16%. Our results highlight the key role played by subsidy specifications in determining the trade-off between insulation and fuel switch, e.g. insulation investments doubles, and heat pump adoption is 19% lower, when subsidies are restricted to the most comprehensive measures. Finally, alternative assumptions regarding the availability of renewable energy sources—biogas in particular—imply stronger energy efficiency efforts.