We want to go from Champ de Mars tour Eiffel to Versailles Chateau Rive Gauche on the latest train possible. We want to see the tower at night but then go back to our hotel in Versailles. Do you know the times of night trains on the RER c

11:08 pm / 23:08 is the last RER C train from Champ de Mars station to Versailles Rive Gauche.  Note that this is from May 2, 2023 onwards.  There are rail maintenance works ongoing currently (April 23 - May 1, 2023) that will affect evening RER C trains between Paris & Versailles, interrupting/ending service earlier than usual.
 
There is one more train from Javel RER C station (one stop further south along the line) that departs at 00:11 to Versailles Rive Gauche.  But, after that the next train is 05:38 in the morning from Champ de Mars.