It was, after all, the "language of diplomacy" in the modern era, due to its specific and unambiguous use of vocabulary and grammar. It would make more sense if the Federation, being a diplomatically-oriented organization, adapt French as its primary language.
it makes me wonder though, why English became standard rather than one of the existing galactic powers. Certainly there was already some form of "Galactic Language" in use before earth joined the interstellar community. If you're looking for a unambiguous, logical language it would probably be Vulcanian.
But then again maybe we westerners just did what we do best; visit some place and then obliterate their culture with our ethnocentrism.
I suppose this could explain the "no wonder they were conquered" comment from McCoy. Even though in another episode Spock said they could never conceive of a conqueror.