Comment by adrian_b

Fischer-Tropsch is based on the reaction of carbon monoxide with dihydrogen (free hydrogen). This mixture is known as syngas.

While now the cheapest way is to make syngas from methane or from coal, it is possible to make syngas from carbon dioxide that reacts with electrolytic hydrogen.

It is also possible to make equivalent precursors of synthetic hydrocarbons by the electrolysis of carbon dioxide in water.

For these 2 methods, you do not need any fossil fuels, but only electrical energy for electrolysis.

Where the energetic efficiency is still very low is when you want to use clean air as the source of CO2, instead of using a concentrated source of CO2. With very cheap energy, i.e. solar energy that is used at the point of capture, it should still be possible to devise a method of capture for CO2 from the air. Many such methods are known, their only problem being a high energy consumption per the amount of captured CO2, so they are impractical with energy that must be bought from the grid, but I do not see why they could not work when coupled directly with solar panels.