The extension of the RER E to the west should connect the Saint-Lazare station to the Nanterre-La Folie station by 2024. To reach Mantes-la-Jolie, however, it will be necessary to wait until 2025.
Direct daytime train between Paris and Berlin will be on the rails in December 2023, as announced by SNCF and Deutsche Bahn to the AFP. An alternative to air travels and another reason to visit the German capital city or the French one if you have not already!