If we look outside of the organisation of the EU, it probably wouldn't make a lot of difference. English will still dominate as a second language, because of American and to a lesser degree English cultural dominance. For example there are very few German tv shows, movies or music populair in the Netherlands and the influence of France has evaporated even more. As a consequence of this many people in the Netherlands don't speak German anymore and France is completely disappearing as a 3rd/4th language. It has even seriously been suggested to stop teaching French in high school. I have no doubt this will not change. Besides culture, the English language English will still dominate the economic and financial world. London is the economic and financial core of Europe, while New York it is for .....well..... the world. English will still dominate the scientific world. Basicly outside the organisation of the EU English will still dominate.
Within the EU itself German and France will try to dominate and become the most important language within the organisation. I think especialy the French will try to enforce their language, but I think it the smaller states, especialy Scandinavia and the Netherlands, but probably also the eastern European states will resist it. They will either force English to become the number one language or complete equality for all languages. So I expect some minor language struggle within the EU, which ends with all languages becoming equal, while no language will dominate. Lets face it everybody speaks English, while most people don't speak either French or German.