We're traveling in June, and our hotel is a 10-minute walk from Sainte Chappelle. I'd thought we might try to do our timed-entry at Sainte Chappelle first thing (9:00) and then the Conciergerie the following day at their opening time of 9:30. I realize there is a joint ticket available, but we plan to have the Paris Museum Pass for me and my husband, and our 16-year-old will be free.
The question is, does this make sense to do, or is there joint security, so that once you've gone through for one you should just stay for the other?