The closest Metro station is actually an
RER C train line station called Versailles-Rive Gauche located here.
You can purchase a ticket for this trip from a ticket window within the station (or from a ticket vending machine using Euro coins). Cost will be 2,90€.
Take the RER C in direction Massy-Palaiseau or Versailles-Chantiers until station
Pont de Garigliano, where you'll want to switch to Tram T3, which you'll want to take until
Porte d'Orleans. This is the most direct route. You'll have to buy a different type of ticket for the Tram, a
Ticket t+, since the tickets for RER trains are not valid for Trams nor buses unfortunately.