The EU has a €300B program directly subsidizing farmers [0]. To quote the wiki page:

     The [EAGF] consumes a large part of the general budget of the European Union. 

Apparently the overarching CAP program consumes something like 30+% of the budget, so I'd love to know what you consider "heavily subsidized" if this doesn't merit.

[0] https://en.wikipedia.org/wiki/European_Agricultural_Guarante...