Containing global warming to 1.5°C implies to stay on a given carbon budget, and therefore to be able to design net zero carbon buildings by 2050. A case study corresponding to a French residential building is used to assess the feasibility of achieving this target. Starting from an actual construction built in 2016, various improvement measures are studied: lowering heating energy needs, implementing bio-sourced materials and renewable energy systems (geothermal heat pump, solar domestic hot water production, and photovoltaic electricity production). Dynamic thermal simulation is used to evaluate energy consumption as well as overheating risk in hot periods. Greenhouse gases emissions are quantified using consequential life cycle assessment approach, considering that during a transition period, exporting electricity avoids impacts corresponding to a marginal production on the grid. Avoided impacts decrease and become zero when the grid is ultimately "decarbonized". From this point, the building should be net zero emission but there remain unavoidable emissions. Residual GHG (greenhouse gases) emissions account for 5.6 kgCO2eq/m² annually. The possibility to offset these emissions is investigated, considering sequestration in forests or vegetation systems. A net zero emission level can be achieved but on a national level, it would require that the whole sequestration potential of forest growth is devoted to offset emissions of new construction. Circular economy for construction products and equipment and considering water use will be needed to further decrease environmental impacts.