Train connections from Versailles to Vernon

No matter how you cut it, to get from Versailles to Vernon, you need to go to Paris first. The most direct is from Versailles Rive Droite to Paris St Lazere and change to Vernon. Back to Paris from Vernon is direct.

Those are local trains, so they won't show up on the SNCF site for long-haul trains,

Try this link. It'll give you some basic info. From Versaille to Mantes La Jolie to Vernon.

France works on a sort of spoke system of transport where you change lines in Paris or sometimes other large cities. Because Vernon and Versailles are on different lines out of Paris, you have to return to Paris to get to Vernon.

Thank you for all your replies. The link to local train schedules most appreciated .