its busy (10min pirate line) but not mega busy, though around that time you may get schools out and also school summer trips, so its hard to say, the general rule of thumb is when the french and english schools are in session, the park is quietish
though it is not always the case.
this year June has been very very busy on weekends because Disney has sold a lots of cheap Dated Tickets for those May and June Weekends and they were all sold out so it was packed on week end and they had to change the schedules of Disneyland Park to 11pm on saturdays .
Thanks for the advice. I'd rather visit during the week for just that reason. I'm wondering if there are any major holidays during that time period - things that would bump attendance up during the week?