Frankly, its simply inconceivable that anyone could regard going to see the Mona Lisa at the Louvre as having any competition from Mickey Mouse at Disneyland.
As for Disneyland, would advise you not to pin too much hope if u have been to others...
Yes...It's free admission on every 1st Sunday of the month for all museums..and of course you would expect huge crowds...however, you would get to enter the museum fast...