When to come — and when to absolutely avoid
By season
Quietest: January and February (excluding the French vacances de février school holiday), and the second half of November. Paris is cold, the daytrippers are gone, and the medieval halls feel as cavernous as they were meant to.
Busiest: April to June and the entire month of October — the European school-trip season. The French vacances in spring (April) and the late-October Toussaint break bring waves of organised groups.
By day of the week
Tuesday and Thursday mornings are calmest. Wednesday afternoons are the worst because French primary schools are out, and the Conciergerie is a classic French school excursion. Saturday late-afternoons after 16:00 are surprisingly quiet — the daytrippers have left and the locals are heading to dinner.
By time of day
The first slot at 09:30 is by far the best. Until about 10:30 you can have the Salle des Gens d'Armes mostly to yourself — and it is the kind of room that benefits from silence. The Marie-Antoinette chapel is calmest in the first hour or in the final hour before close.