Is Parc Astérix inaccessible by public transport? Well, no: there are several bus routes to the theme park, voted France's best theme park for the third year running.
So, off to the Bercy bus station in the 12th arrondissement (accessible by metro lines 6 and 14, "Bercy" stop, then a 10-minute walk, all signposted) to board a Flixbus bus to the nearest bus station to the park ("Parc Astérix" when booking), for just €4.99.
Other bus lines, the Ozeroute buses, are also accessible from the Marne-la-Vallée (77) RER station or from Charles de Gaulle airport (or Beauvais airport, if you're closer), and drop you off at the park's parking lot in Plailly. The latter option is much more expensive, however, with tickets costing around 30 euros (from Beauvais airport) or 20 euros (from Charles de Gaulle airport).
Daily connections are provided by both companies, allowing you to be at the park by opening time, without even needing to rent a car! Come on, how about a ride on the Toutatis or Pegasus Express?