the head of the EU Commission is a conservative, and EPP has the biggest share of seats at the parliament. So what are we talking about?
Europe's idea of conservative is what Americans would call far left. It's all relative anyway. If you're just trying to conserve something left wing against something even farther left wing then it's still left. Mostly meaningless label. Almost no one even knows where the political terms left and right came from. People call Afghanistan right wing as if that means something.