All they need to do is remove the parking spots and there will be plenty of space for trees.

I don't know about other EU urban centers but I feel this can be done with better street and square planning.

Narrowing roads so avenues/thoroughfares can be lined with trees, or better yet, move the avenues underground so the roof can be used for green public space. Using more green when renovating public squares. Moving (more) parking spaces underground.

My old home city of Antwerp recently renovated a bunch of public squares and instead of using the opportunity to reintroduce a lot of green, many of the squares are grey tiled or concrete wastelands that act like a blinding open grill in summer, with just a couple of new growth trees for show. A recent large new "park" is not much more than a giant grassland and concession stands with half a dozen trees, not much shade to be found.

Asking the real question here.

In most European cities, if you could free up 30% of space you should probably use most of it for housing.

This would also avoid people commuting from far away, thus saving a ton of energy and CO2 emissions. The CO2 captured by a 20-year tree through its growth is probably emitted in a few months max by a single suburban car commuter.