The first Sunday of the month is free, as everybody knows. Therefore, to avoid the crowds, the best time to go is on the day before - everyone's waiting for the free entry the next day!
We went on the Saturday and had the place to ourselves, apart from the usual crowd that is always gathered around the Mona Lisa. We went again on the Sunday and it was hideously busy. We didn't have to queue though: a nice security guard spotted our pushchair and let us jump the queue! It's a surprisingly child-friendly place, and of course the advantage of the free Sunday is that you can take the kids (they are always free on any day) and you haven't wasted the cost of your ticket if their behaviour is such that you have to leave after five minutes.
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