"Has the EU done much space travel?"
Hell yes! The EU neatly planted its flag on Titan. That's a moon of SATURN, not the low-hanging fruit that the Earth's moon is. It also has its flag sitting on a comet. Try and hit that softly as a target.
ESA, unlike the other agencies, is not into propaganda. It's into hard science. Also, you can't beat the European launcher Ariane in reliability.