In a hypothetical year 2193 where the European Union has coalesced into a single superstate for many decades...

In a hypothetical year 2193 where the European Union has coalesced into a single superstate for many decades, what would be the most likely de facto federal language of such European Federation?

English? French? German?

All of them.

Arabic

Russian.

I reckon all of them would be official (along with other languages from former sovereign nations) and that these would be used on the estate level, but which one would likely be used the most by the central government? It's very unlikely that they would continue a multilingual model indefinitely due to how inefficient that would prove to be (i.e., having to translate every single memo exchanged within the house of government to god knows how many languages).

My personal guess is that English could be used as a "neutral" alternative to French and German by the central government, considering its global status, its spread in Europe and its close ties to both languages.

Most, if not all languages will have some official standing, but the language of mutual communication/government will be a toss-up between English and French.

If Brexit means Brexit then French for sure.

Would Germany really allow French to become the language of government when German-speaking regions are both more populated and represent a larger share of the GDP?

I know the de facto capital Brussels (which is unlikely to be moved due to the nice neutral position) is mostly French speaking though.

Why would they switch to French when English is still by far the most common second language in the EU?

French is simply more widely known, making it naturally better at mutual communication between languages.

English is obviously better at this, as a German and an Italian will use English as their medium to talk to each other more often than not, but French can fill the same role should England not participate in a European Federation.

Spanish or English.