The countries which have English as a second language.... were both British colonies until the 1960's. Malta had once even pondered integrating into the United Kingdom, though later gained independence and became a Republic. Cyprus has some undergraduate education in English (a friend of mine from Kuwait had gone to college there).
That just means that 3 or more are already on the plan. With the UK gone it s not even an issue of rivalry anymore. The eu could promote this as a means to facilitate international trade, and frankly i dont see why members would disagree since it s already de facto happening
Other European countries don't have that history.