Yes, why French? From this
2010 news article, it doesn't seem like French has any special status in Vatican diplomatic business.
"Vatican officials usually write (and speak) to each other in Italian. When writing to bishops in other countries, they’ll often use the language of that country—French for France, English for the United States, etc. Latin is generally reserved for letters that are especially important or official as opposed to casual correspondence."
Are there some awkward seating juxtapositions that would result from applying Italian or Latin alphabetical order?