Well, I suppose a FEW cardinals and similar types probably try their hand at speaking Latin in the Vatican, but I've been there and I can tell you that mostly they just speak Italian.
As for French, Spanish, Italian, etc. If you've studied any Latin (which I have), you'd know that they are now quite distinct. They share a basic root vocabulary and syntactic structure, but there have been numerous sound changes, grammatical modifications/simplifications, and vocabulary additions. I doubt very much whether a Roman (even one from Late Antiquity, and disregarding the obvious vocabulary problems) hearing modern French would have any clue what was being said (at least at first).
Now, getting back to the question posed.... I think it would be great if Latin were the international language of scholarship. As things stand today, we grad students have to learn French, Italian and German (or others like Spanish, Chinese, or Arabic depending on one's field) just to be able to read scholarly works written by the international community. I think it would be a lot easier if some all-powerful authority could just decree that we all had to learn Latin and write our dissertations in that. Even though Latin's a helluva language (but don't even get me STARTED on ancient Greek

) it's still preferable to having to learn a host of modern tongues you never plan on speaking!
Of course in a few decades we'll probably have good enough translation software to make all this irrelevant...