Trains in the direction of Vézelay depart from the small Paris Bercy Station, which is close to the much larger and more well-known Paris Gare de Lyon Station.
From Gare de Lyon to Paris Bercy Station it is about a 1 km walk, via the Rue de Bercy, or take the Metro, line 14 to "Bercy" (the first stop after Gare de Lyon).
Attention: pickpockets, especially on busy platforms and in the trains of the subway!
Alternative: by Flixbus to Auxerre (train station) and from there continue by train.
Get off at Sermizelles-Vézelay station. From there a bus goes to Vézelay.
This is the Route Planner of the French Railways (SNCF) (English)
Choose "To" Sermizelles-Vézelay, if you continue on foot from this station (more connections), or: Vézelay, if you continue by bus (less connections).