I get what you're saying but that's a non-issue. At plenary meeting and conferences every country is in the same situation, they communicate via an Armada of interpreters, just like they do at the UN, at the WTO, the WHO, the NATO, and so on. Outside of those they communicate in English and/or French.
If a Greek newspaper is sending a journalist who can't speak English or French they sent the wrong person. If a local government sends a politician into the EU who can't communicate in English or French they sent the wrong person. Also, it would already be sufficient for the cause if Greek newspapers would put the spotlight on GREEK politicians in Brussels. So far not even THAT is happening in a sufficient manner...
> But IMO pre-Brexit a big reason the British government had a lot of influence over the British press (and vice-versa) while the EU government didn't was the simple issue of speaking the same language and being in the same city.
Every single press-Release of the EU is done in English language. Granted, the EU doesn't invite to press-conferences in London to talk to the local press, that's the job of the local government.
Pre-Brexit it would have been the job of the British government to promote the spirit of "We are European", but as everywhere it is more useful to their narrative to promote "We are Nationalists!"