I would poke my eyes out before I would go to Louvre on the free sunday again.. or even consider Versailles that day. I think the free sundays are best used by visiting some lesser known musuems.. ones that may, or may not interest you, if you leave after 1/2 hr you don't feel like you've lost out money, and you can visit several small, less crowded sites that way.
If you go on a weekend( fountain shows are Saturday and Sundays) you will need to purchase a supplement ticket for the formal gardens where the fountain show is.. its about 8 euros and you can purchase it there , lines for that are not bad since you are already in the grounds having passed through the palace with your Museum pass already.
I would go on the Friday.. I would aim to arrive at palace at least 45 minutes before it opens, with pass in hand you can get right in security line( which will already start to form even that early).. that way you can hopefully get through palace in the first wave before it becomes the crushing mass of humanity it turns into very soon after opening.
If you can't go Friday morning before it opens,, then I would go later in day,, say around 1, do gardens and Marie Antionettes Hamlet and Trianons,, then visit the palace after 3 when crowds inside subside.. SLIGHTLY.
This assumes you are planning this visit for the busy season April-October.
PS.. Free sundays for some sights do not start till after height of season so check websites to be sure for places like Louvre etc.