Actually, when you talk about "dimishing relevance", that is almost exactly part of the French motivation for the EU. Facing inevitably increasing global inconsequentiality after WW2, the UK decided to piggyback on the USA (and hence the lingering Euroskepticism) and France decided to forge a new power bloc which - at least at the time - it could dominate, although Germany eventually surpassed it anyway.
But the thing is, languages are more organic than that. They will naturally flow with power. English has probably already peaked globally. Mandarin will supplant it as lingua franca in the Far East and spreading out further - even potentially to places like Africa and South America. I suspect English will remain sufficiently dominant around the Atlantic. But even still, within the EU, there will be a natural tendency to gravitate to a common, useful language. If the UK remains absent (I think it will rejoin, ultimately) plus the gently widening divide with the US, there is a likelihood English will decline and use of EU languages increase. In the end, Germany as the strongest nation plus Austria, Switzerland, and the Germanic languages of the Low Countries and Scandinavia make it a strong choice, although French has the legacy of having been a major lingua franca, much higher global use, and probably more common in other major countries like Spain and Italy.