Free trade is neither left nor right.
Labor unions can support protectionism in the benefit of the industries where they work.
However, protectionism can also mean more expensive goods for the low class and higher profits for some business.
Free trade redistributes income for the upper class in rich countries and for the low class in the poor countries.
Center-left economist Paul Krugman has already cricticized the anti-trade ideas of the far right politican Pat Buchanan.
Every economist support free trade as a rule. Some of them consider that this rule should have no exception. Some of them consider that there is an ecxetion: some temporary protectionism is acceptable for infant industries.
European agriculture is not an infant industry (actually, it is a very old industry). However, the argument for the protection of the European agriculture is not economic.
I had to quit reading when I saw the words "center" and "Paul Krugman" anywhere near each other.