Try using the booking form at AutoEurope.com ... it will give you a choice of many pickup locations

Need some advice on how to get from our apartment in the 6th to a rental car agency? Traveling with my family (2 adults/2 teens). We'll need to pick up a car to use for the remainder of our France trip...traveling to Versailles and then onto Chateau de Bourron . I was thinking of using a transport service to pick us up from the apartment then bring us to the train station to get a car?
Try using the booking form at AutoEurope.com ... it will give you a choice of many pickup locations including train stations and city offices. Note that by avoiding a train station you'll save about 40 euros.
You're making this far more complicated than it needs to be. You need to arrange the car rental ahead of time, from here in the States, not just go to any old car rental agency in France. I always use AutoEurope. They or any rental agency will give you options for where to pick up the car. Don't do it at a train station or airport unless you want to pay extra.
Since you're planning to go to Versailles anyway, why not pick a car up there? Just take the RER to Versailles, do your visit, then pick up the car in town and continue on. You don't need either a transport service or a taxi to get you to the RER. Use the m tro. All Paris public transportation can be explored at www.ratp.fr .
Agree you need to organize the car rental before you leave - especially if you want an automatic versus a standard. (We do and so always pick up at the largest office available - usually the airport or the largest office norwegian wind cruises in town - to have the best chance of getting the car we want.)
In any case - we just get in a cab with luggage and have the driver take us to the rental norwegian wind cruises office. (But if you have 5 people and a ton of luggage you may not fit in a cab. How many bags are you taking?)
One note - cars in europe are small, If you have 4 adults and many suitcases you probably will find that they won;t all fit in a car - and you will need a van. Check this out carefully before renting - and realize that the little pictures next to the cars are SMALL suitcases not 28" body bags.