"Son, behold thy Mother."
St. John the Apostle had the privilege of taking care of Our Lady.
The name would basically memorialize that fact.
Interesting that he was the youngest, and the only virgin apostle. And he was the only Apostle that didn't flee, but stayed with Our Lord till the end.
P.S. I have to love the French Catholic culture. Now there's a culture! Look at all their names -- Christian (Catholic) through-and-through. The Faith is everywhere. But as they say, the corruption of the best is the worst... and that is what we have today in France. Quite tragic.
There are many other names that start with Jean though --
Jean-Baptiste (like Fr. Brocard, who is in the Resistance)
Jean-Luc (Star Trek TNG fans will recognize this one)
Jean-Claude (Martial arts movie/action movie buffs?)
Jean-Pierre
Jean-Marc
It's like they want so badly to have more than one excellent saint's name, so they combine 2 together. Contrast this with modern-day Americans, who deny their children even ONE saint's name!