It's unclear if "Europe" wants anything of the sort at this point, and you seem to assume that English would be the common language, which is not unreasonable since it's the one currently being used, but it's not politically acceptable, and it'll be worse if the UK finally decides to leave.
Note also that Europe is probably the part of the world where minority languages are in better shape. E.g Catalan is spoken by 4 million native speakers, which is more than all of the native american language speakers combined.
Even if there are more minority languages in SE Asia and South America, I'm not sure they're treated better there than in Europe.
By the way, I know it's HN and people here are more internationalized and pro-globalisation than the average but the actual reality on the ground is that the far right and nationalism is growing in most EU countries and the current trend is to limit the EU, not expand it even further.
And that is not to say English is in any way a good language. It is dreadful. But language is not valuable for how well it pleases a gramaticist, but for its ability to facilitate communication, and right now English is so far and away #1 globally in that regard doing anything but trying to press every civilization to teach their citizens it is almost condemning them to poverty for some upper crust and downright selfish ideals of cultural diversity.
Europe may want to achieve some things in common but not at the expense of not achieving other things not in common.
Per the article: step outside the European worldview to see how cultural viewpoints elsewhere understand and express the value of multilingualism