Centrists, I'd say. Same as the people pushing it in the UK.
The left, the anti-immigration parties and really, any party which isn't wholly 'let's do the same as we've always had' probably imagine that this would be used to their disadvantage somehow.
The EU is definitely more right than left after the last election. The Commission in particular, though it seems they're always more right-wing than the Parliament. As we speak they're watering down all sorts of regulations beneficial to the common citizen but inconvenient to the corporations, and the "moderate" right is now openly threatening to ally, or downright allying, with the far right in various right-wing matters in order to get them passed.
