All in all, you're on your own, my friend, and, unless you already are a superstar, you'll probably get royally ignored! You're gonna have to put in some effort (and frustration!) if you are eager to integrate, as the French are extremely family centered and they wouldn't risk their secure universe for anything in the world, not even for your overly smiling, nice self!
In these circumstances, two main solutions are presenting to you:
one is to produce some children, if you are inclined to, which will give you a strategic advantage considering that children represent more than a quarter of all Versailles population (compared with about one fifth, in Paris). And let me tell you something: this is a society revolving around children! All the efforts are deployed so the precious little ones receive the best education, the best healthcare, food, experiences, the best of everything! "Year after year, the biggest fear in the life of a parent is that their child's school is not the best one" once told me a mother, neighbor of mine, after prodigiously teaching the childless audience all we ever wanted to know about children and we were afraid to ask.
As a parent, you'll get the chance to meet other parents just about everywhere (all of them experts in child rearing and more than readily available to give advice on anything - parenting related or not) and finally get invited to children birthday parties, parents' evenings out and other enriching activities. It's useless to say that if you manage to trick a French into producing that precious heir with you, all of your social pains will be greatly alleviated, YOU ARE IN!!!
The second (and less life committed) socializing solution is to have been on the 8th of September at the Avenue de Paris (you know, the one flanked by the City Hall on one side and the castle looking down on everyone, the other side) where the Forum des Associations was being held. If you weren't there, you are one of the few unlucky as there is only one occasion in Versailles when you can see more locals gathered together (=the Bastille Day's party).
There are more than 650 established associations in Versailles, that is, one for about 130 inhabitants, which means that, taking into account the private lessons and other activities, virtually everyone subscribed to one form or another of socializing pastime: economic, religious, cultural, humanitarian, social, sportive, hobbies, you name it. They were all present and a lot of them have royal in the name - it's hard to miss the Malta Order, or "Le scrabble du roy", "Le brochet du roy" (king's pike), "Cercle d'échecs le Roi Soleil" (Sun King Chess Club) or the "Charlemagne" association (providing school teaching help). Vive le Roi!!!
The new (and quite expensive) associative year is about to start. Don't miss it or you'll be doomed to loneliness and pity parties for an entire year!
Oh, and to see that things are changing around here, if you ever move to Versailles just write me, okay? I might invite you to a newcomer's apéro (or dinner, if you're lucky).