As Protagonist said there is only one RV park that's close. But close is a relative term. How about across the river and you ride the ferry across to the French Quarter.
If this idea appeals to you consider staying at Bayou Segnette S.P.
from there it's only a few miles to the ferry landing and you can ride that across the river. Don't know if the state park is already booked during that time.
There are a couple ferry systems and they pick up in different locations and have varying times of operation. Be sure to check it out online.