If I can make 1 unit of food for €50 and use 50 tons of carbon, or make it for €60 and use 10 tons of carbon, a carbon tax and food subsidy would allow me to sell that €60 low carbon food for €50 and force me to sell the high carbon food for €60
This gives an economic incentive to use the lower carbon method, funded by those who use more carbon, while not changing the end price or output.
Just to provide the numbers: in 2030, a tax will be introduced of 120 DKK (~16€) / ton CO2e, which linearly increases each year until it reaches 300 DKK (~40€) / ton CO2e in 2035. However, the farmers can get subsidies for changing their practices and adopting new technologies, in order to reduce their emissions. I.e., the government will give you money to change your production, so you can minimize the carbon taxes you have to pay. There are more technicalities to how it works, but that's the gist of it. The important part is that the goal is to transition to new technologies and production methods, which reduces emissions per unit food produced.
There will be no food subsidy, however, and a rough estimate of the increase of food cost is something like 1.5%, with beef having the highest increase. Take this estimate with a grain of salt though, as it's difficult to estimate. An increase in food cost is expected though.