Weekends are very full at DLP year round.
Beware -- French schools do not have classes on Wednesdays, so if you go during the week while school is still in session in June, do not go on a Wednesday for the lightest crowds.
The lightest crowds by far are on Mondays and Tuesdays.
DLP has become the number one European tourist attraction in numbers of visitors per day. This number swells on weekends, no matter what the weather, year round.
Some things to keep in mind -- a "busy" weekend in June will be a lot like a day rated an 8 or 9 at Walt Disney World...and the lines work much differently -- Europeans don't queau quietly and pleasantly -- it's more of a funnel effect -- in fact, some of them don't "get" the americanized Disney line system and you will get crowding around the line entrances, and a lot of horseplay back and forth between the lines as they pass each other. There are also a lot of smokers in line. Telling them to put them out will get you nowhere. Just ignore it and hold your breath until you have passed by them.
Use the fastpasses whenever possible -- and for the major attractions you will HAVE to use the fastpasses.....Things like Crushes Coaster can easily run up to 120 minutes wait (it does not have fast passes)...it is routinely at 45 - 70 minutes on NON peak days...
The times listed for waits are more accurate than those in the American parks...sometimes at WDW when it says 20 minutes, the wait is actually 5 minutes. At DLP the queu lines can wrap around themselves several times, and when it says Space Mountain 70 minute wait, it IS a 70 minute wait, even though the line might look very short outside. It weaves around, up and down, and back around inside the building.
Also, keep in mind that if you want to ride the train, you need to board it at the Main Street station, not in it's Fantasyland stop. Europeans see the train as a "ride" and not as transportation. If you wait at the back train station thinking you will save the walk and take it back to the front of the park, you will be out of luck when nobody departs the very crowded train and you wait for the next one. Similarly, the Paddlewheel -- it's seen as a major ride and more people crowd on to ride it than they do in the US parks where it is seen as a time-filler.
But don't be afraid of going even on a busy day. The parks have a lot to see -- there are plenty of quiet places to sit and reflect, grab lunch, watch the crowds. If you don't get on a ride you don't get on the ride. Two absolutely not to miss are Phantom Manor and Pirates of the Carribean -- they are much much better at DLP than in the US parks and the lines are manageable, even on crowded days. Space Mountain is very different from the US version -- it is a full-fledged inversion/corkscrew coaster, not the mini-coaster found inside the US version. That means, if your young ones are not ready for a coaster in the dark that flips upside down, then it's not a ride for them. It's similar to Rock'N Roller Coaster in that matter.
Another thing to keep in mind -- Europeans, for the most part, start at one place (either To the right, or to the left) and then proceed around the park, doing each attraction in order. Americans tend to cut back and forth across the park and use a similar strategy as that in the US parks -- the same general strategy works in DLP as well.
One final caveat: DLP now has EMH hours every single morning -- that means when the park opens to the general public, that the line queus can often already be filled with DLP's resort guests, especially for the major attractions.
On an off-peak day, it is possible to do both parks and ride every attraction, including minor ones and a few repeats and even include a show or two, by 4:00 pm. On a peak day, you'll be lucky to cover half the attractions in one single park by the end of the day. To that end, Disney has achieved what is has wanted to do -- keep you returning a second day for the other park rather than doing both of them in one day and running out of things to do.